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

Cross-spectral analysis of the X-ray variability of Mrk 421

Using the cross-spectral method, we confirm the existence of the X-ray hard lags discovered with cross-correlation function technique during a large flare of Mrk 421 observed with BeppoSAX . For the 0.1--2 versus 2--10keV light curves, both methods suggest sub-hour hard lags. In the time domain, the degree of hard lag, i.e., the amplitude of the 3.2--10 keV photons lagging the lower energy ones, tends to increase with the decreasing energy. In the Fourier frequency domain, by investigating the cross-spectra of the 0.1--2/2--10 keV and the 2--3.2/3.2--10 keV pairs of light curves, the flare also shows hard lags at the lowest frequencies. However, with the present data, it is impossible to constrain the dependence of the lags on frequencies even though the detailed simulations demonstrate that the hard lags at the lowest frequencies probed by the flare are not an artifact of sparse sampling, Poisson and red noise. As a possible interpretation, the implication of the hard lags is discussed in the context of the interplay between the (diffusive) acceleration and synchrotron cooling of relativistic electrons responsible for the observed X-ray emission. The energy-dependent hard lags are in agreement with the expectation of an energy-dependent acceleration timescale. The inferred magnetic field (B ~ 0.11 Gauss) is consistent with the value inferred from the Spectral Energy Distributions of the source. Future investigations with higher quality data that whether or not the time lags are energy-/frequency-dependent will provide a new constraint on the current models of the TeV blazars.Comment: 11 pages, 6 figures, accepted by MNRA

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

biogas from municipal solid waste landfills a simplified mathematical model

Abstract Municipal solid waste (MSW) landfills now represent one of the most important issues related to the waste management cycle. Knowledge of biogas production is a key aspect for the proper exploitation of this energy source, even in the post-closure period. In the present study, a simple mathematical model was proposed for the simulation of biogas production. The model is based on first-order biodegradation kinetics and also takes into account the temperature variation in time and depth as well as landfill settlement. The model was applied to an operating landfill located in Sicily, in Italy, and the first results obtained are promising. Indeed, the results showed a good fit between measured and simulated data. Based on these promising results, the model can also be considered a useful tool for landfill operators for a reliable estimate of the duration of the post-closure period

Assessment of out-of-plane strength of masonry infills through a FE augmented dataset

Evaluation of the out-of-plane strength of infilled frames is a matter of fundamental importance. In fact, by observing post-earthquake damage, it has been noted that infills subject to in-plane and out-of-plane inertial forces may achieve collapse due to out-of-plane actions. This mode of collapse may result quite dangerous to the people in the proximity of a building subjected an earthquake. The possibility to perform an accurate safety assessment is fundamental to prevent this type of failure. Different expressions for evaluating the out-of-plane resistance of infilled frames are available in the literature. These are based on analytical formulations validated on the basis of too limited or too large experimental datasets. This implies that these expressions are often conflicting, showing good reliability in some cases and less in others. In order to overcome this drawback, this paper provides the definition of a hybrid database obtained by merging existing experimental test data with additional ones obtained from numerical simulations by means of a refined FE micro-model. A new data-driven empirical expression for estimating the OOP resistance of infilled frames has been developed based on the hybrid database so developed. The new expression has the advantage of taking into account the aspect ratio of the filled frame, the influence of vertical loads, and the influence of the out-of-plane load application mode. Finally, validation tests are performed against experimental and numerical samples

Seismic analysis and risk mitigation of existing constructions

Following a thorough and lengthy procedure, we would like to thank all contributors for their highest calibre papers, which comprise the Special Issue on \u201cSeismic analysis and risk mitigation of existing constructions\u201d of the Open Construction and Building Technology Journal. The topic of the Special Issue encompasses a large number of issues spanning the design of special interventions for the reduction of the effects of earthquakes on civil structures and infrastructures, to the structural identification and assessment issues. The field of seismic engineering is continuously looking for new strategies and methods, which empower the designers and make them able to obtain more accurate response predictions. Researchers are involved in this process and are called to successfully encounter new challenges emerging from the increasing need for the assessment of existing constructions, especially when assuming strategic roles. As is also reflected by the papers presented in the Special Issue, the continuous advances of the research in this field moves across two basic directions. On the one hand, there is the direction of the robustness and the reliability of the recent nonlinear seismic assessment methods (static, dynamic, incremental dynamic). Several approaches can be followed to predict the response of structures to strong ground motions; however the results coming from each of them are in some cases conflicting and not always amenable to easy interpretation. On the other hand, the reliability of structural models still remains a major task of structural engineering and of seismic engineering in particular. Mathematical models have to reproduce the physics of structures and its evolution during complex damaging processes. Global and local models tend to reflect this by minimizing the loss of information. In the Special Issue, we are proud to present state-of-the-art research findings described in detail in 9 papers authored by 27 researchers of different universities in Italy, California (USA), Greece and United Kingdom. The papers deal with the seismic analysis and risk mitigation aiming to address different purposes by proposing numerical, analytical approaches and experimental tests

Cost and EAL based optimization for seismic reinforcement of RC structures

In this paper, a new genetic algorithm-based framework aimed at efficiently design multiple seismic retrofitting interventions is proposed. The algorithm focuses on the minimization of retrofitting intervention costs of reinforced concrete (RC) frame structures. The feasibility of each tentative solution is assessed by considering in an indirect way the expected annual loss (EAL), this evaluation is performed by referring to different limit states whose repairing costs are expressed as a percentage of reconstruction costs and evaluating the respective mean annual frequency of exceedance. As the EAL takes into account the overall structural performances, to involves both serviceability and ultimate limit states, two different seismic retrofitting techniques are considered. In particular, FRP wrapping of columns is employed to increase the ductility of RC elements managing life safety and collapse limit state demands. On the other hand, steel bracings are used to increase the global stiffness of the structure and mainly increase operational and damage limit states performances. The optimization procedure is carried out by the novel genetic algorithm-based framework developed in Matlab® that is connected to a 3D RC frame fiber-section model implemented in OpenSees. For both the retrofitting systems, the algorithm provides their position within the structure (topological optimization) and their sizing. Results will show that seismic retrofitting can be effectively designed to increase the overall structural safety by efficaciously optimizing the intervention costs