Operators in Rigged Hilbert spaces: some spectral properties

A notion of resolvent set for an operator acting in a rigged Hilbert space \D \subset \H\subset \D^\times is proposed. This set depends on a family of intermediate locally convex spaces living between \D and \D^\times, called interspaces. Some properties of the resolvent set and of the corresponding multivalued resolvent function are derived and some examples are discussed.Comment: 29 page

Intermittent aeration in a hybrid moving bed biofilm reactor for carbon and nutrient biological removal

The paper presents an experimental study on a lab scale hybrid moving bed biofilm reactor with intermittent aeration. Specifically, a comparison between two different operating conditions was analyzed: continuous and intermittent aeration. Both continuous and intermittent aeration were monitored and compared in order to get the best operational conditions. The intermittent aeration campaign was sub-divided in three phases with different duration of alternation of aerobic and anoxic times and organic and nitrogen loading rates. The effciency of N-removal improved by 70% during the intermittent aeration. The best condition was observed with 40 min of aeration and 20 min of no-aeration, an organic loading rate of 2.2 kgCODm-3day-1 and a nitrogen loading rate of 0.25 kgNm-3day-1: under these operational conditions the removal effciencies for carbon and nitrogen were 93% and 90%, respectively. The derived results provide the basis for WWTP upgrade in order to meet stricter euent limits at low energy requirements

Simultaneous nitrogen and organic carbon removal in aerobic granular sludge reactors operated with high dissolved oxygen concentration

Simultaneous nitrification and denitrification (SND) together with organic removal in granules is usually carried out without Dissolved Oxygen (DO) concentration control, at ‘‘low DO’’ (with a DO < 30–50% of the saturation value, about 3–4 mg/L) to promote anoxic conditions within the aggregates. These conditions can sometimes be in detrimental of the stability of the granules itself due to a lack of shear force. In this work, the authors achieved SND without oxygen control with big sized granules. More spe- cifically, the paper presents a experimentation focused on the analysis of two Sequencing Batch Reactors (SBRs), in bench scale, working with different aerobic sludge granules, in terms of granule size, and high DO concentration, (with concentration varying from anoxic conditions, about DO 0 mg/L, to values close to those of saturation, >7–8 mg/L, during feast and famine conditions respectively). In particular, different strategies of cultivation and several organic and nitrogen loading rate have been applied, in order to eval- uate the efficiencies in SND process without dissolved oxygen control. The results show that, even under conditions of high DO concentration, nitrogen and organic matter can be simultaneously removed, with efficiency >90%. Nevertheless, the biological conditions in the inner layer of the granule may change sig- nificantly between small and big granules, during the feast and famine periods. From point of view of granule stability, it is also interesting that with a particle size greater than 1.5 mm, after the cultivation start-up, the granules are presented stable for a long period (about 100 days) and, despite the variations of operational conditions, the granules breaking was always negligible

Foaming in membrane bioreactors: Identification of the causes

Membrane bioreactors (MBRs) represent by now a well established alternative for wastewater treatment. Their increasing development is undoubtedly related to the several advantages that such technology is able to guarantee. Nevertheless, this technology is not exempt from operational problems; among them the foaming still represents an “open challenge” of the MBR field, due to the high complexity of phe- nomenon. Unfortunately, very little work has been done on the foaming in MBRs and further studies are required. Actually, there is not a distinct difference between conventional activated system and MBR: the main difference is that the MBR plants can retain most Extracellular Polymeric Substances (EPSs) in the bioreactor. For these reason, unlike conventional activated sludge systems, MBRs have experienced foaming in the absence of foam-forming micro-organisms. Nevertheless, the actual mechanisms of EPS production and the role of bacteria in producing foam in activated sludge in MBRs are still unclear. In this paper, the authors investigated the roles of EPS and foam-forming filamentous bacteria by analyzing samples from different pilot plants using MBRs. In particular, in order to define the macroscopic features and the role of EPS and filamentous bacteria, a Modified Scum Index (MSI) test was applied and pro- posed. Based on the MSI and the foam power test, the causes of biological foaming were identified in terms of the potential for foaming, the quality and the quantity of the foam. The results indicated that the MBR foaming was influenced significantly by the concentration of bound EPSs in the sludge. In addition, the quantity and stability of MBR scum increased when both bound EPSs and foam-forming filamentous bacteria were present in the activated sludge

Fouling mechanism elucidation in membrane bioreactors by bespoke physical cleaning

Cake layer deposition on a membrane surface can determine both external and internal membrane fouling through negatively affecting the total filtration resistance while exerting a positive effect as a pre-filter. Membranes are usually subjected to a periodic cake layer removal through routine physical cleaning, specifically permeate backwashing of hollow fiber membranes, or enhanced cleaning through, for example, chemically-enhanced backwashing. Physical cake layer removal is crucial for sustaining permeability, yet the effect of different physical cleaning modes remains poorly evaluated. The present work attempts to analyze physical cake layer removal through the application of specific cleaning methods and the impact of these on the subsequent resistance. The constituent contributions to the overall resistance are appraised by means of the Resistances In-Series model, with the aim of producing a robust protocol for quantifying these discrete contributors. The results, based in part on published data, show the proposed approach to reliably determine the relative contribution of the different resistance components to within 0.1 · 1012 m−1 across a range of different bench and pilot-scale plants, confirming the resilience of the method

Influence of the Height of Municipal Solid Waste Landfill on the Formation of Perched Leachate Zones

Waste settlement as well as consolidation phenomena, which occur inside a landfill for municipal solid waste (MSW), can cause a decrease in waste permeability. This can lead to a reduction in conveyance of the leachate drainage system. It is therefore possible that a so-called perched leachate zone will form. Such a zone is constituted by an area in the body of the landfill where the leachate is temporarily trapped and is unable to infiltrate downward. This phenomenon is influenced by many factors, which include rain infiltration rate, waste moisture and composition, landfill height, and so on. The main aim of the paper is to elucidate the role played by landfill height in the formation of perched leachate zones using a one-dimensional (1D) mathematical model. The model allows for the simulation of the perco- lation fluxes throughout an MSW landfill based on mass-balance equations. The results showed a different response in terms of flow rates throughout the landfill, highlighting the important role of landfill height in the formation of perched leachate zones. Landfill height influences not only the formation of perched leachate zones but also their extension throughout the body of the landfill

Mechanical behavior of carbon/flax hybrid composites for structural applications

In this work, the influence of an unidirectional carbon fabric layer on the mechanical performances of bidirectional flax fabric/epoxy composites used for structural applications was studied. Two different bidirectional flax fabrics were used to produce flax fabric reinforced plastic (FFRP) laminates by a vacuum bagging process: one is normally used to make curtains; the other, heavier and more expensive than the previous one, is usually used as reinforcement in composite structures. In order to realize hybrid structures starting from FFRP, an unidirectional UHM carbon fabric was used to replace a bidirectional flax fabric. Tensile and three-point bending tests were performed to evaluate the mechanical properties of the laminates investigated (both FFRP and hybrids). Furthermore, the mechanical behavior of the different bidirectional flax fabrics was analyzed by carrying out tensile tests. The experimental tests showed that the structures reinforced with flax fabrics, normally used to make curtains, present better flexural properties than that of others while, in tensile configuration, these last show higher modulus and strength. Moreover, both FFRP laminates show low mechanical properties, which do not allow their use in structural applications while the presence of one external layer of unidirectional carbon involves remarkable increase in their properties. According to this study, the hybrid composites realized could be used in several structural applications (i.e., nautical and automotive)