We propose a non-standard numerical method for the solution of a system of integro-differential equations describing an epidemic of an infectious disease with behavioral changes in contact patterns. The method is constructed in order to preserve the key characteristics of the model, like the positivity of solutions, the existence of equilibria, and asymptotic behavior. We prove that the numerical solution converges to the exact solution as the step size h of the discretization tends to zero. Furthermore, the method is first-order accurate, meaning that the error in the discretization is O(h), it is linearly implicit, and it preserves all the properties of the continuous problem, unconditionally with respect to h. Numerical simulations show all these properties and confirm, also by means of a case-study, that the method provides correct qualitative information at a low computational cost
Numerous real-world phenomena involve the interplay between processes of production and decay or consumption and can be therefore modeled by positive and conservative Production-Destruction differential Systems (PDS). Patankar-type schemes are linearly implicit integrators specifically designed for PDS with the aim of retaining, with no restrictions on the stepsize, the positivity of the solution and the linear invariant of the system. In this work we extend the Patankar technique, already established for Runge-Kutta and deferred correction methods, to multistep schemes. As a result, we introduce the class of Modified Patankar Linear Multistep (MPLM) methods, for which a thorough investigation of the convergence is carried out. Furthermore, we design an embedding procedure for the computation of the Patankar weights and prove the high order of convergence of the resulting MPLM scheme. A comparative study on the simulation of selected test cases highlights the competitive performance of the MPLM methods with respect to other Patankar-type discretizations.
Patankar-type schemes, Positivity-preserving, High order, Conservativity, Linear multistep methods
Divertor Tokamak Test facility project: status of design and implementation
Romanelli F.
;
Abate D.
;
Acampora E.
;
Agguiaro D.
;
Agnello R.
;
Agostinetti P.
;
Agostini M.
;
Aimetta A.
;
Albanese R.
;
Alberti G.
;
Albino M.
;
Alessi E.
;
Almaviva S.
;
Alonzo M.
;
Ambrosino R.
;
Andreoli P.
;
Angelone M.
;
Angelucci M.
;
Angioni C.
;
Angrisani Armenio A.
;
Antonini P.
;
Aprile D.
;
Apruzzese G.
;
Aquilini M.
;
Aragone G.
;
Arena P.
;
Ariola M.
;
Artaserse G.
;
Aucone L.
;
Augieri A.
;
Auriemma F.
;
Ayllon Guerola J.
;
Badodi N.
;
Baiocchi B.
;
Balbinot L.
;
Baldacchini C.
;
Balestri A.
;
Barberis T.
;
Barone G.
;
Barucca L.
;
Baruzzo M.
;
Begozzi S.
;
Belardi V.
;
Belli F.
;
Belpane A.
;
Beone F.
;
Bertolami S.
;
Bianucci S.
;
Bifaretti S.
;
Bigioni S.
;
Bin W.
;
Boccali P.
;
Boeswirth B.
;
Bogazzi E.
;
Bojoi R.
;
Bollanti S.
;
Bolzonella T.
;
Bombarda F.
;
Bonan M.
;
Bonanomi N.
;
Bonaventura A.
;
Boncagni L.
;
Bonesso M.
;
Bonfiglio D.
;
Bonifetto R.
;
Bonomi D.
;
Borgogno D.
;
Borzone T.
;
Botti S.
;
Boz E.
;
Braghin F.
;
Brena M.
;
Brezinsek S.
;
Brombin M.
;
Bruschi A.
;
Buonocore S.
;
Buratti P.
;
Buratti P.
;
Busi D.
;
Calabro G.
;
Caldora M.
;
Calvo G.
;
Camera G.
;
Campana G.
;
Candela S.
;
Candela V.
;
Cani F.
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Cantone L.
;
Capaldo F.
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Cappello S.
;
Caponero M.
;
Carchella S.
;
Cardinali A.
;
Carnevale D.
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Carraro L.
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Carrelli C.
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Casalegno V.
;
Casiraghi I.
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Castaldo C.
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Castaldo A.
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Castro G.
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Carpignano A.
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Causa F.
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Cavazzana R.
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Cavedon M.
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Cavenago M.
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Cecchini M.
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Ceccuzzi S.
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Celentano G.
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Celona L.
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Centioli C.
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Centomani G. V.
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Cesaroni S.
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Chiariello A. G.
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Chomicz R.
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Cianfarani C.
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Cichocki F.
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Cinque M.
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Cioffi A.
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Ciotti M.
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Cipriani M.
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Ciufo S.
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Claps V.
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Claps G.
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Coccorese V.
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Coccorese D.
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Colangeli A.
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Coltella T.
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Consoli F.
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Cordella F.
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Corradini D.
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Costa O.
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Crea F.
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Cremona A.
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Crescenzi F.
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Crisanti F.
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Cristofari G.
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Croci G.
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Cucchiaro A.
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D'Ambrosio D.
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Dal Molin M.
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Dalla Palma M.
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Dane F.
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Day C.
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De Angeli M.
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De Leo V.
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De Luca R.
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De Marchi E.
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De Marzi G.
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De Masi G.
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De Nardi E.
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De Piccoli C.
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De Sano G.
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De Tommasi G.
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Del Nevo A.
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Delfino A.
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Della Corte A.
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Deodati P.
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Desiderati S.
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Di Ferdinando E.
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Di Florio M. G.
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Di Gironimo G.
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Di Grazia L. E.
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Di Marzo V.
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Di Paolo F.
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Di Pietro E.
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Di Pietrantonio M.
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Di Prinzio M.
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Di Silvestre A.
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Di Zenobio A.
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Dima R.
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Domenichelli A.
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Doria A.
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Dose G.
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Dubbioso S.
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Dulla S.
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Duran I.
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Eboli M.
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Elitropi M.
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Emanuelli E.
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Esposito B.
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Ettorre P.
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Fabbri C.
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Fabbri F.
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Fadone M.
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Faggiano M. M.
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Falcioni F.
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Falessi M. V.
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Fanale F.
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Fanelli P.
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Fassina A.
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Fassina A.
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Favaretto M.
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Favero G.
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Ferraris M.
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Ferrazza F.
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Ferretti C.
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Ferro A.
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Ferron N.
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Fiamozzi Zignani C.
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Figini L.
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Filippi F.
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Fimiani A.
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Fiorenza F.
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Gobbin M.
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Gorini G.
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Granucci G.
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Grasso D.
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Grasso T.
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Grazioso S.
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Greuner H.
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Griva G.
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Grosso G.
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Guerini S.
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Gunn J. P.
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Hauer V.
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Hidalgo Salaverri J.
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Hoppe M.
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Laguardia L.
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Li J.
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Locati F.
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Lorenzini R.
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Lotto L.
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Loureiro J.
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Lucca F.
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Luda Di Cortemiglia T.
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Maccari P.
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Manca G.
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Manfrin S.
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Manganelli M.
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Mantica P.
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Marin A.
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Martone R.
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Marucci A.
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Masala V.
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Mauro G.
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Meineri C.
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Mele A.
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Menicucci I.
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Messina G.
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Mezi L.
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Moro A.
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Moro A.
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Muraro A.
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Pizzuto A.
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Platania P.
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Polimadei A.
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Villone F.
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Vivio F.
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Vlad G.
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Wischmeier M.
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Wu H. S.
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Wyss I.
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Zanino R.
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Zaniol B.
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Zanon F.
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Zappatore A.
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Zavarise G.
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Zito P.
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Zoppoli A.
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Zucchetti M.
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Zuin M.
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Zumbolo P.
An overview is presented of the progress since 2021 in the construction and scientific programme preparation of the Divertor Tokamak Test (DTT) facility. Licensing for building construction has been granted at the end of 2021. Licensing for Cat. A radiologic source has been also granted in 2022. The construction of the toroidal field magnet system is progressing. The prototype of the 170 GHz gyrotron has been produced and it is now under test on the FALCON facility. The design of the vacuum vessel, the poloidal field coils and the civil infrastructures has been completed. The shape of the first DTT divertor has been agreed with EUROfusion to test different plasma and exhaust scenarios: single null, double null, X-divertor and negative triangularity plasmas. A detailed research plan is being elaborated with the involvement of the EUROfusion laboratories.
An X-ray Diffraction pattern consists of the relevant information (the signal) and the noisy background. Under the assumption that they behave as the components of a two-dimensional mixture (bicomponent fluid) having slightly different physical properties related to the density-gradients, a Lattice Boltzmann Method is applied to disentangle the two different diffusive dynamics. The solution is numerically stable, computationally not demanding and, moreover, it provides an efficient increase of the signal-to-noise ratio for patterns blurred by poissonian noise and affected by collection data anomalies (fiber-like samples, experimental setup, etc.). The model has been succesfully applied to different resolution images. Ke
Cyber risk is a significant concern for all types of businesses. The consequences of a cyber attack can be quite severe. Investing in security to mitigate the impact of such risks is a crucial task, both in terms of the frequency and the severity of cyber incidents. In this paper, we propose a practical application of the Gordon and Loeb model, thereby suggesting a methodology to estimate risk exposure and reconsidering some investment evaluation metrics. Our findings strongly support the claim that maximizing the expected net benefit of an investment solely at the optimal level is not sufficient for sound decision-making. On the contrary, incorporating metrics that evaluate the benefit in relation to risk and consider worst-case scenarios offers deeper insights
cyber risk, security economics, security investments, risk exposure, Gordon-Loeb model
Duval B. P.
;
Abdolmaleki A.
;
Agostini M.
;
Ajay C. J.
;
Alberti S.
;
Alessi E.
;
Anastasiou G.
;
Andrebe Y.
;
Apruzzese G. M.
;
Auriemma F.
;
Ayllon-Guerola J.
;
Bagnato F.
;
Baillod A.
;
Bairaktaris F.
;
Balbinot L.
;
Balestri A.
;
Baquero-Ruiz M.
;
Barcellona C.
;
Bernert M.
;
Bin W.
;
Blanchard P.
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Boedo J.
;
Bolzonella T.
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Bombarda F.
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Boncagni L.
;
Bonotto M.
;
Bosman T. O. S. J.
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Brida D.
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Brunetti D.
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Buchli J.
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Buerman J.
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Buratti P.
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Burckhart A.
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Busil D.
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Caloud J.
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Camenen Y.
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Cardinali A.
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Carli S.
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Carnevale D.
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Carpanese F.
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Carpita M.
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Castaldo C.
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Causa F.
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Cavalier J.
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Cavedon M.
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Cazabonne J. A.
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Cerovsky J.
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Chapman B.
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Chernyshova M.
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Chmielewski P.
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Chomiczewska A.
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Ciraolo G.
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Coda S.
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Colandrea C.
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Contre C.
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Coosemans R.
;
Cordaro L.
;
Costea S.
;
Craciunescu T.
;
Crombe K.
;
Dal Molin A.
;
D'Arcangelo O.
;
de Las Casas D.
;
Decker J.
;
Degrave J.
;
de Oliveira H.
;
Derks G. L.
;
di Grazia L. E.
;
Donner C.
;
Dreval M.
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Dunne M. G.
;
Durr-Legoupil-Nicoud G.
;
Esposito B.
;
Ewalds T.
;
Faitsch M.
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Farnik M.
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Fasoli A.
;
Felici F.
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Ferreira J.
;
Fevrier O.
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Ficker O.
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Frank A.
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Fransson E.
;
Frassinetti L.
;
Fritz L.
;
Furno I.
;
Galassi D.
;
Galazka K.
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Galdon-Quiroga J.
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Galeani S.
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Galperti C.
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Garavaglia S.
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Garcia-Munoz M.
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Gaudio P.
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Gelfusa M.
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Genoud J.
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Gerru Miguelanez R.
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Ghillardi G.
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Giacomin M.
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Gil L.
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Gillgren A.
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Giroud C.
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Golfinopoulos T.
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Goodman T.
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Gorno S.
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Grenfell G.
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Gruca M.
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Gyergyek T.
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Hafner R.
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Hamed M.
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Hamm D.
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Han W.
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Harrer G.
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Harrison J. R.
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Hassabis D.
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Henderson S.
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Hennequin P.
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Hidalgo-Salaverri J.
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Hogge J. -P.
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Hoppe M.
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Horacek J.
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Huber A.
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Huett E.
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Iantchenko A.
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Innocente P.
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Ionita-Schrittwieser C.
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Ivanova Stanik I.
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Jablczynska M.
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van Vuuren A. J.
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Jardin A.
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Jarleblad H.
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Jarvinen A. E.
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Kalis J.
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Karimov R.
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Karpushov A. N.
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Kavukcuoglu K.
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Kay J.
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Kazakov Y.
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Keeling J.
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Kirjasuo A.
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Koenders J. T. W.
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Kohli P.
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Komm M.
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Kong M.
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Kovacic J.
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Kowalska-Strzeciwilk E.
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Krutkin O.
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Kudlacek O.
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Kumar U.
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Kwiatkowski R.
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Labit B.
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Laguardia L.
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Laszynska E.
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Lazaros A.
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Lee K.
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Lerche E.
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Linehan B.
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Liuzza D.
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Lunt T.
;
Macusova E.
;
Mancini D.
;
Mantica P.
;
Maraschek M.
;
Marceca G.
;
Marchioni S.
;
Mariani A.
;
Marin M.
;
Marinoni A.
;
Martellucci L.
;
Martin Y.
;
Martin P.
;
Martinelli L.
;
Martinelli F.
;
Martin-Solis J. R.
;
Masillo S.
;
Masocco R.
;
Masson V.
;
Mathews A.
;
Mattei M.
;
Mazon D.
;
Mazzi S.
;
Mazzi S.
;
Medvedev S. Y.
;
Meineri C.
;
Mele A.
;
Menkovski V.
;
Merle A.
;
Meyer H.
;
Mikszuta-Michalik K.
;
Miron I. G.
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Molina Cabrera P. A.
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Moro A.
;
Murari A.
;
Muscente P.
;
Mykytchuk D.
;
Nabais F.
;
Napoli F.
;
Nem R. D.
;
Neunert M.
;
Nielsen S. K.
;
Nielsen A.
;
Nocente M.
;
Noury S.
;
Nowak S.
;
Nystrom H.
;
Offeddu N.
;
Olasz S.
;
Oliva F.
;
Oliveira D. S.
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Orsitto F. P.
;
Osborne N.
;
Dominguez P. O.
;
Pan O.
;
Panontin E.
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Papadopoulos A. D.
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Papagiannis P.
;
Papp G.
;
Passoni M.
;
Pastore F.
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Pau A.
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Pavlichenko R. O.
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Pedersen A. C.
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Pedrini M.
;
Pelka G.
;
Peluso E.
;
Perek A.
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Von Thun C. P.
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Pesamosca F.
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Pfau D.
;
Piergotti V.
;
Pigatto L.
;
Piron C.
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Piron L.
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Pironti A.
;
Plank U.
;
Plyusnin V.
;
Poels Y. R. J.
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Pokol G. I.
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Poley-Sanjuan J.
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Poradzinski M.
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Porte L.
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Possieri C.
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Poulsen A.
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Pueschel M. J.
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Putterich T.
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Quadri V.
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Rabinski M.
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Ragona R.
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Raj H.
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Redl A.
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Reimerdes H.
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Reux C.
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Riedmiller M.
;
Rienacker S.
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Rigamonti D.
;
Rispoli N.
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Rivero-Rodriguez J. F.
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Madrid C. F. R.
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Rueda J. R.
;
Ryan P. J.
;
Salewski M.
;
Salmi A.
;
Sassano M.
;
Sauter O.
;
Schoonheere N.
;
Schrittwieser R. W.
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Sciortino F.
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Selce A.
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Senni L.
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Sharapov S.
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Sheikh U. A.
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Sieglin B.
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Silva M.
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Silvagni D.
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Schmidt B. S.
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Solano E. R.
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Sozzi C.
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Spolaore M.
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Spolladore L.
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Stagni A.
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Strand P.
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Sun G.
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Suttrop W.
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Svoboda J.
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Tal B.
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Tala T.
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Tamain P.
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Tardocchi M.
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Biwole A. T.
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Tenaglia A.
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Terranova D.
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Testa D.
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Theiler C.
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Thornton A.
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Thrysoe A. S.
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Tomes M.
;
Tonello E.
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Torreblanca H.
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Tracey B.
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Tsimpoukelli M.
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Tsironis C.
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Tsui C. K.
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Ugoletti M.
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Vallar M.
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van Berkel M.
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van Mulders S.
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van Rossem M.
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Venturini C.
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Veranda M.
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Verdier T.
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Verhaegh K.
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Vermare L.
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Viezzer E.
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Villone F.
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Vincent B.
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Vincenzi P.
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Voitsekhovitch I.
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Votta L.
;
Vu N. M. T.
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Wang Y.
;
Wang E.
;
Wauters T.
;
Weiland M.
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Weisen H.
;
Wendler N.
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Wiesen S.
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Wiesenberger M.
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Wijkamp T.
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Wuthrich C.
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Yadykin D.
;
Yang H.
;
Yanovskiy V.
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Zebrowski J.
;
Zestanakis P.
;
Zuin M.
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Zurita M.
;
Ricci D.
Tokamak à configuration variable (TCV), recently celebrating 30 years of near-continual operation, continues in its missions to advance outstanding key physics and operational scenario issues for ITER and the design of future power plants such as DEMO. The main machine heating systems and operational changes are first described. Then follow five sections: plasma scenarios. ITER Base-Line (IBL) discharges, triangularity studies together with X3 heating and N2 seeding. Edge localised mode suppression, with a high radiation region near the X-point is reported with N2 injection with and without divertor baffles in a snowflake configuration. Negative triangularity (NT) discharges attained record, albeit transient, βN ∼ 3 with lower turbulence, higher low-Z impurity transport, vertical stability and density limits and core transport better than the IBL. Positive triangularity L-Mode linear and saturated ohmic confinement confinement saturation, often-correlated with intrinsic toroidal rotation reversals, was probed for D, H and He working gases. H-mode confinement and pedestal studies were extended to low collisionality with electron cyclotron heating obtaining steady state electron iternal transport barrier with neutral beam heating (NBH), and NBH driven H-mode configurations with off-axis co-electron cyclotron current drive. Fast particle physics. The physics of disruptions, runaway electrons and fast ions (FIs) was developed using near-full current conversion at disruption with recombination thresholds characterised for impurity species (Ne, Ar, Kr). Different flushing gases (D2, H2) and pathways to trigger a benign disruption were explored. The 55 kV NBH II generated a rich Alfvénic spectrum modulating the FI fas ion loss detector signal. NT configurations showed less toroidal Alfvén excitation activity preferentially affecting higher FI pitch angles. Scrape-off layer and edge physics. gas puff imaging systems characterised turbulent plasma ejection for several advanced divertor configurations, including NT. Combined diagnostic array divertor state analysis in detachment conditions was compared to modelling revealing an importance for molecular processes. Divertor physics. Internal gas baffles diversified to include shorter/longer structures on the high and/or low field side to probe compressive efficiency. Divertor studies concentrated upon mitigating target power, facilitating detachment and increasing the radiated power fraction employing alternative divertor geometries, optimised X-point radiator regimes and long-legged configurations. Smaller-than-expected improvements with total flux expansion were better modelled when including parallel flows. Peak outer target heat flux reduction was achieved (>50%) for high flux-expansion geometries, maintaining core performance (H98 > 1). A reduction in target heat loads and facilitated detachment access at lower core densities is reported. Real-time control. TCV’s real-time control upgrades employed MIMO gas injector control of stable, robust, partial detachment and plasma β feedback control avoiding neoclassical tearing modes with plasma confinement changes. Machine-learning enhancements include trajectory tracking disruption proximity and avoidance as well as a first-of-its-kind reinforcement learning-based controller for the plasma equilibrium trained entirely on a free-boundary simulator. Finally, a short description of TCV’s immediate future plans will be given.
In this paper, we describe an upgrade of the Alya code with up-to-date parallel linear solvers capable of achieving reliability, efficiency and scalability in the computation of the pressure field at each time step of the numerical procedure for solving a Large Eddy Simulation formulation of the incompressible Navier–Stokes equations. We developed a software module in the Alya’s kernel to interface the libraries included in the current version of PSCToolkit, a framework for the iterative solution of sparse linear systems, on parallel distributed-memory computers, by Krylov methods coupled to Algebraic MultiGrid preconditioners. The Toolkit has undergone various extensions within the EoCoE-II project with the primary goal of facing the exascale challenge. Results on a realistic benchmark for airflow simulations in wind farm applications show that the PSCToolkit solvers significantly outperform the original versions of the Conjugate Gradient method available in the Alya’s kernel in terms of scalability and parallel efficiency and represent a very promising software layer to move the Alya code toward exascale.
The project of the Visible Spectroscopy diagnostics for the Zeff radial profile measurement and for the divertor visible imaging spectroscopy, designed for the new tokamak DTT (Divertor Tokamak Test), is presented. To deal with the geometrical constraints of DTT and to minimize the diagnostics volume inside the access port, an integrated and compact solution hosting the two systems has been proposed. The Zeff radial profile will be evaluated from the Bremsstrahlung radiation measurement in the visible spectral range, acquiring light along ten Lines of Sight (LoS) in the upper part of the poloidal plane. The plasma emission will be focused on optical fibers, which will carry it to the spectroscopy laboratory. A second equipment, with a single toroidal LoS crossing the plasma centre and laying on the equatorial plane, will measure the average Zeff on a longer path, minimizing the incidental continuum spectrum contaminations by lines/bands emitted from the plasma edge. The divertor imaging system is designed to measure impurity and main gas influxes, to monitor the plasma position and kinetics of impurities, and to follow the plasma detachment evolution. The project aims at obtaining the maximum coverage of the divertor region. The collected light can be shared among different spectrometers and interferential filter devices placed outside the torus hall to easily change their setup. The system is composed of two telescopes, an upper and a lower one, allowing both a perpendicular and a tangential view of the DTT divertor region. This diagnostic offers a unique and compact solution designed to cope the demanding constraints of this next-generation tokamak fusion devices, integrating essential tools for wide-ranging impurity characterization and versatile investigation of divertor physics.
In this paper, we introduce new generalized barycentric coordinates (coined as moment coordinates) on convex and nonconvex quadrilaterals and convex hexahedra with planar faces. This work draws on recent advances in constructing interpolants to describe the motion of the Filippov sliding vector field in nonsmooth dynamical systems, in which nonnegative solutions of signed matrices based on (partial) distances are studied. For a finite element with n vertices (nodes) in R2, the constant and linear reproducing conditions are supplemented with additional linear moment equations to set up a linear system of equations of full rank n, whose solution results in the nonnegative shape functions. On a simple (convex or nonconvex) quadrilateral, moment coordinates using signed distances are identical to mean value coordinates. For signed weights that are based on the product of distances to edges that are incident to a vertex and their edge lengths, we recover Wachspress coordinates on a convex quadrilateral. Moment coordinates are also constructed on a convex hexahedra with planar faces. We present proofs in support of the construction and plots of the shape functions that affirm its properties.
Filippov vector field
generalized barycentric coordinates
hexahedron
mean value coordinates
quadrilateral
Wachspress coordinates
Numerical simulation of fractional-order partial differential equations is a challenging task and the majority of computing environments does not provide support for these problems. In this paper we describe how to exploit some of the Matlab features (a programming language not supporting fractional calculus in a naive way) to solve partial differential equations with the spectral fractional Laplacian. For shortness we focus on fractional Poisson equations but the proposed approach can be extended, with just some technical difficulties, to more involved problems. This approach cannot be considered as a highly efficient and accurate way to solve fractional partial differential equations, but as an easy-to-use tool for non specialists in numerical computation to obtain solutions without having to produce sophisticated numerical codes.
2024Contributo in volume (Capitolo o Saggio)metadata only access
MEG
Arcara G.
;
Pellegrino G.
;
Pascarella A.
;
Mantini D.
;
Kobayashi E.
;
Jerbi K.
Magnetoencephalography (MEG) is a valuable non-invasive neurophysiology technique for investigation of brain function and dysfunction. In this chapter, we will discuss the main characteristics of MEG signals, and the great potential it offers for scientific interrogation in psychology, cognitive neuroscience, neurology, and neuropsychiatry. Starting from the physical properties of MEG recordings, the chapter will highlight the main advantages of utilizing MEG in neuroscience (that is a combination of very high temporal resolution and good spatial resolution) and will summarize the current status of MEG in research and clinical settings. To make this topic more relatable to widely available electroencephalography (EEG), we will present several comparisons of MEG with EEG. The objective of the present chapter is to provide a broad overview of the principle concepts and strengths of MEG, aimed at newcomers to the field.
Brain Mapping
Electrophysiology
Magnetencephalography
Magnetic Fields
MEG
Source estimation
Deep learning is a powerful tool for solving data driven differential problems and has come out to have successful applications in solving direct and inverse problems described by PDEs, even in presence of integral terms. In this paper, we propose to apply radial basis functions (RBFs) as activation functions in suitably designed Physics Informed Neural Networks (PINNs) to solve the inverse problem of computing the perydinamic kernel in the nonlocal formulation of classical wave equation, resulting in what we call RBF-iPINN. We show that the selection of an RBF is necessary to achieve meaningful solutions, that agree with the physical expectations carried by the data. We support our results with numerical examples and experiments, comparing the solution obtained with the proposed RBF-iPINN to the exact solutions.
We study the implementation of a Chebyshev spectral method with forward Euler integrator proposed in Berardi et al.(2023) to investigate a peridynamic nonlocal formulation of Richards’ equation. We prove the convergence of the fully-discretization of the model showing the existence and uniqueness of a solution to the weak formulation of the method by using the compactness properties of the approximated solution and exploiting the stability of the numerical scheme. We further support our results through numerical simulations, using initial conditions with different order of smoothness, showing reliability and robustness of the theoretical findings presented in the paper.
In this paper we address the existence, uniqueness and approximation of solutions of delay differential equations (DDEs) with Carathéodory type right-hand side functions. We provide construction of the randomized Euler scheme for DDEs and investigate its error. We also report results of numerical experiments.
Carathéodory type conditions
Delay differential equations
Existence and uniqueness
Randomized Euler scheme
Physics-Informed Neural Networks (PINN) are a machine learning tool that can be used to solve direct and inverse problems related to models described by Partial Differential Equations by including in the cost function to minimise during training the residual of the differential operator. This paper proposes an adaptive inverse PINN applied to different transport models, from diffusion to advection–diffusion–reaction, and mobile–immobile transport models for porous materials. Once a suitable PINN is established to solve the forward problem, the transport parameters are added as trainable parameters and the reference data is added to the cost function. We find that, for the inverse problem to converge to the correct solution, the different components of the loss function (data misfit, initial conditions, boundary conditions and residual of the transport equation) need to be weighted adaptively as a function of the training iteration (epoch). Similarly, gradients of trainable parameters are scaled at each epoch accordingly. Several examples are presented for different test cases to support our PINN architecture and its scalability and robustness.
Inverse problems
Mobile–immobile model
Physics-informed neural networks
Porous material
Transport in porous media
We discuss the dynamics of a (neutral) test particle in topological star spacetime undergoing scattering processes by a superposed test radiation field, a situation that in a 4D black hole spacetime is known as relativistic Poynting-Robertson effect, paving the way for future studies involving radiation-reaction effects. Furthermore, we study self-force-driven evolution of a scalar field, perturbing the top-star spacetime with a scalar charge current. The latter for simplicity is taken to be circular, equatorial and geodetic. To perform this study, besides solving all the self-force related problem (regularization of all divergences due to the self-field, mode sum regularization, etc.), we had to adapt the 4D Mano-Suzuki-Takasugi formalism to the present 5D situation. Finally, we have compared this formalism with the (quantum) Seiberg-Witten formalism, both of which are related to the solutions of a Heun confluent equation but appear in different contexts in the literature: the first in black hole perturbation theory and the second in quantum curves in super-Yang-Mills theories.
Topological star spacetime, massless scalar field perturbations
Using the multipolar post-Minkowskian formalism, we compute the frequency-domain waveform generated by the gravitational scattering of two nonspinning bodies at the fourth post-Minkowskian order (O(G4), or two-loop order), and at the fractional second post-Newtonian accuracy [O(v4/c4)]. The waveform is decomposed in spin-weighted spherical harmonics and the needed radiative multipoles, Um(ω),Vm(ω), are explicitly expressed in terms of a small number of master integrals. The basis of master integrals contains both (modified) Bessel functions, and solutions of inhomogeneous Bessel equations with Bessel-function sources. We show how to express the latter in terms of Meijer G functions. The low-frequency expansion of our results is checked against existing classical soft theorems. We also complete our previous results on the O(G2) bremsstrahlung waveform by computing the O(G3) spectral densities of radiated energy and momentum, in the rest frame of one body, at the thirtieth order in velocity.
In this paper we present an approach to compute analytical post-Minkowskian corrections to unbound two-body scattering in the self-force formalism. Our method relies on a further low-velocity (post-Newtonian) expansion of the motion. We present a general strategy valid for gravitational and nongravitational self-force, and we explicitly demonstrate our approach for a scalar charge scattering off a Schwarzschild black hole. We compare our results with recent calculations in [L. Barack, Comparison of post-Minkowskian and self-force expansions: Scattering in a scalar charge toy model, Phys. Rev. D 108, 024025 (2023)PRVDAQ2470-001010.1103/PhysRevD.108.024025], showing complete agreement where appropriate and fixing undetermined scale factors in their calculation. Our results also extend their results by including in our dissipative sector the contributions from the flux into the black hole horizon.
