Positive solutions of Schr\"odinger equations and fine regularity of boundary points

Given a Lipschitz domain $\Omega$ in ${\mathbb R} ^N$ and a nonnegative potential $V$ in $\Omega$ such that $V(x)\, d(x,\partial \Omega)^2$ is bounded in $\Omega$ we study the fine regularity of boundary points with respect to the Schr\"odinger operator $L_V:= \Delta -V$ in $\Omega$. Using potential theoretic methods, several conditions equivalent to the fine regularity of $z \in \partial \Omega$ are established. The main result is a simple (explicit if $\Omega$ is smooth) necessary and sufficient condition involving the size of $V$ for $z$ to be finely regular. An essential intermediate result consists in a majorization of $\int_A | {\frac {u} {d(.,\partial \Omega)}} | ^2\, dx$ for $u$ positive harmonic in $\Omega$ and $A \subset \Omega$. Conditions for almost everywhere regularity in a subset $A$ of $\partial \Omega$ are also given as well as an extension of the main results to a notion of fine ${\mathcal L}_1 | {\mathcal L}_0$-regularity, if ${\mathcal L}_j={\mathcal L}-V_j$, $V_0,\, V_1$ being two potentials, with $V_0 \leq V_1$ and ${\mathcal L}$ a second order elliptic operator.Comment: version 1. 23 pages version 3. 28 pages. Mainly a typo in Theorem 1.1 is correcte

Coinductive subtyping for abstract compilation of object-oriented languages into Horn formulas

In recent work we have shown how it is possible to define very precise type systems for object-oriented languages by abstractly compiling a program into a Horn formula f. Then type inference amounts to resolving a certain goal w.r.t. the coinductive (that is, the greatest) Herbrand model of f. Type systems defined in this way are idealized, since in the most interesting instantiations both the terms of the coinductive Herbrand universe and goal derivations cannot be finitely represented. However, sound and quite expressive approximations can be implemented by considering only regular terms and derivations. In doing so, it is essential to introduce a proper subtyping relation formalizing the notion of approximation between types. In this paper we study a subtyping relation on coinductive terms built on union and object type constructors. We define an interpretation of types as set of values induced by a quite intuitive relation of membership of values to types, and prove that the definition of subtyping is sound w.r.t. subset inclusion between type interpretations. The proof of soundness has allowed us to simplify the notion of contractive derivation and to discover that the previously given definition of subtyping did not cover all possible representations of the empty type

Some Results on the Boundary Control of Systems of Conservation Laws

This note is concerned with the study of the initial boundary value problem for systems of conservation laws from the point of view of control theory, where the initial data is fixed and the boundary data are regarded as control functions. We first consider the problem of controllability at a fixed time for genuinely nonlinear Temple class systems, and present a description of the set of attainable configurations of the corresponding solutions in terms of suitable Oleinik-type estimates. We next present a result concerning the asymptotic stabilization near a constant state for general $n\times n$ systems. Finally we show with an example that in general one cannot achieve exact controllability to a constant state in finite time.Comment: 10 pages, 4 figures, conferenc

Complex energy networks: Energy-ecological efficiency based evaluations towards the sustainability in energy sector

In the last years, international programs in diverse sectors and national frameworks have been driven by the need of a sustainable growth, in a green economy perspective. In order to reduce the energy losses/dissipations, as well as the fossil fuels employment and related pollutant emissions, indeed, the spread of combined heat and power units and/or renewable sources generators is promoted into both the electrical grids and the thermal networks but are often in conflict with the economic aspects. In this context, the optimal management of complex energy networks - including, in particular, smart district heating - may lead to the achievement of important goals from the environmental and sustainability viewpoints. The aim of this paper is to develop a preliminary methodology for the complete evaluation of complex energy networks, considering energy, economic and environmental aspects. With this purpose, a case study consisting in a network for the fulfillment of electrical and thermal needs of the connected users will be analyzed, considering different scenarios in terms of energy generation mix and operation and applying different optimization software. In addition, the carried out evaluations will allow to set the basis for the discussion about the future of energy policies and possible incentives towards the sustainable development of the energy sector

Performance Increase of a Small-scale Liquefied Natural Gas Production Process by Means of Turbo-expander☆

Abstract In the last years, the growing demand of the energy market has led to the increasing penetration of renewable energy sources in order to achieve the primary energy supply. However, in the next years fossil fuels are expected to remain the dominant energy source, due to the forecasted increase of global energy consumption. In particular, the natural gas is predicted to still play a key role in the energy market, on account of its lower environmental impact than other fossil fuels. Natural gas is currently employed mainly as gaseous fuel for stationary energy generation, but also as liquefied fuel, as an alternative to the diesel fuel, in vehicular applications. Liquefied Natural Gas (LNG) is currently produced in large plants directly located at the extraction sites. The aim of the study is the definition of an optimal small-scale production process for LNG, to be realized – in opposition to the current habit – directly at filling stations. With this purpose, two different LNG production layouts have been proposed and investigated within a thermodynamic analysis: starting from a Joule-Thompson LNG expansion process, a new layout with a turbo-expander has been proposed for the natural gas liquefaction. The carried-out simulations show that the new proposed solution allow to optimize the LNG production process and to minimize the process' energy consumption

Thermodynamic Evaluation of Repowering Options for a Small-size Combined Cycle with Concentrating Solar Power Technology☆

Abstract The increasing penetration of low-carbon technologies and enhancements in fossil-fuelled power plants efficiency are some of the most important and up to date research topics. Renewable energy, in particular solar, has the potential of meeting the world energy needs while addressing environmental concerns, but technological advances in renewable energy electricity production are necessary to become competitive with conventional technologies. New opportunities to increase the penetration of renewables energies, smoothing out renewables variability and intermittency problems, come out from the hybridization concept. Hybrid renewable-fossil fuel systems join the advantages of both renewable energies and programmable devices. Among all the renewable technologies available for hybridization, Concentrating Solar Power (CSP) with parabolic trough is the most diffused because of its relatively conventional technology and ease of scale-up. CSP hybrids are well established worldwide, predominantly with natural gas: the hybridization options for CSP ranging from feed water heating, reheat steam, live steam to steam superheating. Based on a detailed thermodynamic cycle model of a reference small-size one pressure level Combined Cycle (CC) plant, the impact of CSP addition is thoroughly evaluated. Different hybrid schemes are evaluated and compared considering CC off-design operation. The goal of this study is to evaluate, from a thermodynamic point of view, three repowering options of a small-size CC with a CSP system in a hybrid system configuration and to quantify their potential benefits in terms of system's performance increase. In particular, the optimal size of CSP plant is shown for each investigated hybrid repowering options. The changes in CC steam cycle operating parameters are presented together with CC performance increase. It is shown that solar hybridization into an existing CC plant may give rise to a substantial benefit from a thermodynamic point of view

Low-temperature district heating networks for complete energy needs fulfillment

In order to reduce fossil fuels consumption and pollutant emissions, high contribution is given by district heating. In particular, the integration with renewable energy may lead to a significant increase in energy conversion efficiency and energy saving. Further benefits can be achieved with low temperature networks, reducing the heat dissipations and promoting the exploitation of low enthalpy heat sources. The aim of the paper is the analysis of the potential related to the conversion of existing district heating networks, to increase the exploitation of renewables and eliminate pollutant emissions in the city area. Further aim, in this context, is the optimization \u2013 from both energy production and operation management viewpoints \u2013 of a low temperature district heating network for the fulfillment of the connected users\u2019 energy needs. To this respect, a traditional network with a fossil fuel driven thermal production plant has been considered and compared with a low temperature district heating scenario, including geothermal heat pumps, photovoltaic panels and absorption chillers. These scenarios have been analyzed and optimized with a developed software, demonstrating the reduction of primary energy consumption and CO2 pollutant emissions achievable with low temperature networks. In addition, a preliminary economic comparative evaluation on the variable costs has been carried out. Future studies will investigate the economic aspect also from the investment costs viewpoint

Incubation during laser ablation with bursts of femtosecond pulses with picosecond delays

Abstract: We report on an experimental investigation of the incubation effect during irradiation of stainless steel with bursts of ultrashort laser pulses. A series of birefringent crystals was used to split the pristine 650-fs pulses into bursts of up to 32 sub-pulses with time separations of 1.5 ps and 3 ps, respectively. The number of selected bursts was varied between 50 and 1600. The threshold fluence was measured in case of Burst Mode (BM) processing depending on the burst features, i.e. the number of sub-pulses and their separation time, and on the number of bursts. We found as many values of threshold fluence as the combinations of the number of bursts and of sub-pulses constituting the bursts set to give the same total number of impinging sub-pulses. However, existing incubation models developed for Normal Pulse Mode (NPM) return, for a given number of impinging pulses, a constant value of threshold fluence. Therefore, a dependence of the incubation coefficient with the burst features was hypothesized and experimentally investigated. Numerical solutions of the Two Temperature Model (TTM) in case of irradiation with single bursts of up to 4 sub-pulses have been performed to interpret the experimental results

combined heat and power generation systems design for residential houses

Abstract Nowadays cogeneration is recognized as one of the most effective techniques to meet the increasingly stringent requirements regarding energy efficiency increase and energy saving in buildings. In this context, the aim of this study is the definition of reference parameters for the optimal energy systems design in residential applications. To this purpose, a generation scenario with cogeneration units, heat pumps, auxiliary boilers and chillers (both compression and absorption machines) has been set for the fulfillment of residential users' needs (in terms of electrical, thermal and cooling loads). For a given number of involved households, commercial cogeneration units have been selected, sized on the basis of the electrical peak need, and the generation scenario has been optimized by an in-house developed software, obtaining the optimal energy systems design and operation. Then, a parametric analysis has been carried out varying the number of considered households in order to define the optimal range of the energy systems size. In particular, specific values in terms of installed power for household and installed power for unitary peak load have been determined. For completeness, an economic analysis has been finally carried out for the evaluation of the return on investment and of the differential net present value – with respect to a standard generation scenario (only natural gas boilers for thermal needs fulfillment and electricity purchase from the grid for electrical and cooling needs) – considering a time horizon of ten years

Smile platform: An innovative microfluidic approach for on‐chip sample manipulation and analysis in oral cancer diagnosis

Oral cancer belongs to the group of head and neck cancers, and, despite its large diffusion, it suffers from low consideration in terms of prevention and early diagnosis. The main objective of the SMILE platform is the development of a low‐cost device for oral cancer early screening with features of high sensitivity, specificity, and ease of use, with the aim of reaching a large audience of possible users and realizing real prevention of the disease. To achieve this goal, we realized two microfluidic devices exploiting low‐cost materials and processes. They can be used in combination or alone to obtain on‐chip sample preparation and/or detection of circulating tumor cells, selected as biomarkers of oral cancer. The realized devices are completely transparent with plug‐and‐play features, obtained thanks to a highly customized architecture which enables users to easily use them, with potential for a common use among physicians or dentists with minimal training