The COVID-19 pandemic has impacted on every human activity and, because of theurgency of finding the proper responses to such an unprecedented emergency, itgenerated a diffused societal debate. The online version of this discussion was notexempted by the presence of misinformation campaigns, but, differently from whatalready witnessed in other debates, the COVID-19 -intentional or not- flow of falseinformation put at severe risk the public health, possibly reducing the efficacy ofgovernment countermeasures. In this manuscript, we study theeffectiveimpact ofmisinformation in the Italian societal debate on Twitter during the pandemic,focusing on the various discursive communities. In order to extract suchcommunities, we start by focusing on verified users, i.e., accounts whose identity isofficially certified by Twitter. We start by considering each couple of verified users andcount how many unverified ones interacted with both of them via tweets or retweets:if this number is statically significant, i.e. so great that it cannot be explained only bytheir activity on the online social network, we can consider the two verified accountsas similar and put a link connecting them in a monopartite network of verified users.The discursive communities can then be found by running a community detectionalgorithm on this network.We observe that, despite being a mostly scientific subject, the COVID-19 discussionshows a clear division in what results to be different political groups. We filter thenetwork of retweets from random noise and check the presence of messagesdisplaying URLs. By using the well known browser extension NewsGuard, we assessthe trustworthiness of the most recurrent news sites, among those tweeted by thepolitical groups. The impact of low reputable posts reaches the 22.1% in the right andcenter-right wing community and its contribution is even stronger in absolutenumbers, due to the activity of this group: 96% of all non reputable URLs shared bypolitical groups come from this community.
The problem of modeling water flow in the root zone with plant root absorption is of crucial importance in many environmental and agricultural issues, and is still of interest in the applied mathematics community. In this work we propose a formal justification and a theoretical background of a recently introduced numerical approach, based on the shooting method, for integrating the unsaturated flow equation with a sink term accounting for the root water uptake model. Moreover, we provide various numerical simulations for this method, comparing the results with the numerical solutions obtained by MATLAB pdepe.
Quantitative Methods for the Prioritization of Foods Implicated in the Transmission of Hepatititis E to Humans in Italy
Moro, Ornella
;
Suffredini, Elisabetta
;
Isopi, Marco
;
Tosti, Maria Elena
;
Schembri, Pietro
;
Scavia, Gaia
Hepatitis E is considered an emerging foodborne disease in Europe. Several types of foods are implicated in the transmission of the hepatitis E virus (HEV) to humans, in particular, pork and wild boar products. We developed a parametric stochastic model to estimate the risk of foodborne exposure to HEV in the Italian population and to rank the relevance of pork products with and without liver (PL and PNL, respectively), leafy vegetables, shellfish and raw milk in HEV transmission. Original data on HEV prevalence in different foods were obtained from a recent sampling study conducted in Italy at the retail level. Other data were obtained by publicly available sources and published literature. The model output indicated that the consumption of PNL was associated with the highest number of HEV infections in the population. However, the sensitivity analysis showed that slight variations in the consumption of PL led to an increase in the number of HEV infections much higher than PNL, suggesting that PL at an individual level are the top risky food. Uncertainty analysis underlined that further characterization of the pork products preparation and better assessment of consumption data at a regional level is critical information for fine-tuning the most risky implicated food items in Italy.
epidemiology
food safety
hepatitis E virus
mathematical modeling
Convective flows coupled with solidification or melting in water bodies play a major role in shaping geophysical landscapes. Particularly in relation to the global climate warming scenario, it is essential to be able to accurately quantify how water-body environments dynamically interplay with ice formation or melting process. Previous studies have revealed the complex nature of the icing process, but have often ignored one of the most remarkable particularities of water, its density anomaly, and the induced stratification layers interacting and coupling in a complex way in the presence of turbulence. By combining experiments, numerical simulations, and theoretical modeling, we investigate solidification of freshwater, properly considering phase transition, water density anomaly, and real physical properties of ice and water phases, which we show to be essential for correctly predicting the different qualitative and quantitative behaviors. We identify, with increasing thermal driving, four distinct flow-dynamics regimes, where different levels of coupling among ice front and stably and unstably stratified water layers occur. Despite the complex interaction between the ice front and fluid motions, remarkably, the average ice thickness and growth rate can be well captured with the theoretical model. It is revealed that the thermal driving has major effects on the temporal evolution of the global icing process, which can vary from a few days to a few hours in the current parameter regime. Our model can be applied to general situations where the icing dynamics occur under different thermal and geometrical conditions.
Rayleigh–Bénard convection
density anomaly
hydrodynamic turbulence
ice dynamics
solidification
Turbulent emulsions are complex physical systems characterized by a strong and dynamical coupling between small-scale droplets and large-scale rheology. By using a specifically designed Taylor-Couette shear flow system, we are able to characterize the statistical properties of a turbulent emulsion made of oil droplets dispersed in an ethanol-water continuous solution, at an oil volume fraction up to 40Â %. We find that the dependence of the droplet size on the Reynolds number of the flow at a volume fraction of 1Â % can be well described by the Hinze criterion. The distribution of droplet sizes is found to follow a log-normal distribution, hinting at a fragmentation process as the possible mechanism dominating droplet formation. Additionally, the effective viscosity of the turbulent emulsion increases with the volume fraction of the dispersed oil phase, and decreases when the shear strength is increased. We find that the dependence of the effective viscosity on the shear rate can be described by the Herschel-Bulkley model, with a flow index monotonically decreasing with increasing oil volume fraction. This finding indicates that the degree of shear thinning systematically increases with the volume fraction of the dispersed phase. The current findings have important implications for bridging the knowledge on turbulence and low-Reynolds-number emulsion flows to turbulent emulsion flows.
Soft glassy materials such as mayonnaise, wet clays, or dense microgels display a solid-to-liquid transition under external shear. Such a shear-induced transition is often associated with a nonmonotonic stress response in the form of a stress maximum referred to as “stress overshoot.” This ubiquitous phenomenon is characterized by the coordinates of the maximum in terms of stress and strain that both increase as weak power laws of the applied shear rate. Here we rationalize such power-law scalings using a continuum model that predicts two different regimes in the limit of low and high applied shear rates. The corresponding exponents are directly linked to the steady-state rheology and are both associated with the nucleation and growth dynamics of a fluidized region. Our work offers a consistent framework for predicting the transient response of soft glassy materials upon startup of shear from the local flow behavior to the global rheological observables.
Spin-glass dynamics in the presence of a magnetic field: Exploration of microscopic properties
Paga I.
;
Zhai Q.
;
Baity-Jesi M.
;
Calore E.
;
Cruz A.
;
Fernandez L. A.
;
Gil-Narvion J. M.
;
Gonzalez-Adalid Pemartin I.
;
Gordillo-Guerrero A.
;
Iiguez D.
;
Maiorano A.
;
Vincenzo Marinari
;
Martin-Mayor V.
;
Moreno-Gordo J.
;
Muoz-Sudupe A.
;
Navarro D.
;
Orbach R. L.
;
Parisi G.
;
Perez-Gaviro S.
;
Federico Ricci-Tersenghi
;
Ruiz-Lorenzo J. J.
;
Schifano S. F.
;
Schlagel D. L.
;
Seoane B.
;
Tarancon A.
;
Tripiccione R.
;
Yllanes D.
The synergy between experiment, theory, and simulations enables a microscopic analysis of spin-glass dynamics in a magnetic field in the vicinity of and below the spin-glass transition temperature T g. The spin-glass correlation length, ξ(t, t w; T), is analysed both in experiments and in simulations in terms of the waiting time t w after the spin glass has been cooled down to a stabilised measuring temperature T < T g and of the time t after the magnetic field is changed. This correlation length is extracted experimentally for a CuMn 6 at. % single crystal, as well as for simulations on the Janus II special-purpose supercomputer, the latter with time and length scales comparable to experiment. The non-linear magnetic susceptibility is reported from experiment and simulations, using ξ(t, t w; T) as the scaling variable. Previous experiments are reanalysed, and disagreements about the nature of the Zeeman energy are resolved. The growth of the spin-glass magnetisation in zero-field magnetisation experiments, M ZFC(t, t w; T), is measured from simulations, verifying the scaling relationships in the dynamical or non-equilibrium regime. Our preliminary search for the de Almeida-Thouless line in D = 3 is discussed.
Cooling and heating faster a system is a crucial problem in science, technology, and industry. Indeed, choosing the best thermal protocol to reach a desired temperature or energy is not a trivial task. Noticeably, we find that the phase transitions may speed up thermalization in systems where there are no conserved quantities. In particular, we show that the slow growth of magnetic domains shortens the overall time that the system takes to reach a final desired state. To prove that statement, we use intensive numerical simulations of a prototypical many-body system, namely, the two-dimensional Ising model.
Temperature chaos is present in off-equilibrium spin-glass dynamics
Baity-Jesi M.
;
Calore E.
;
Cruz A.
;
Fernandez L. A.
;
Gil-Narvion J. M.
;
Gonzalez-Adalid Pemartin I.
;
Gordillo-Guerrero A.
;
Iniguez D.
;
Maiorano A.
;
Vincenzo Marinari
;
Martin-Mayor V.
;
Moreno-Gordo J.
;
Munoz-Sudupe A.
;
Navarro D.
;
Paga I.
;
Parisi G.
;
Perez-Gaviro S.
;
Federico Ricci-Tersenghi
;
Ruiz-Lorenzo J. J.
;
Schifano S. F.
;
Seoane B.
;
Tarancon A.
;
Tripiccione R.
;
Yllanes D.
Experiments featuring non-equilibrium glassy dynamics under temperature changes still await interpretation. There is a widespread feeling that temperature chaos (an extreme sensitivity of the glass to temperature changes) should play a major role but, up to now, this phenomenon has been investigated solely under equilibrium conditions. In fact, the very existence of a chaotic effect in the non-equilibrium dynamics is yet to be established. In this article, we tackle this problem through a large simulation of the 3D Edwards-Anderson model, carried out on the Janus II supercomputer. We find a dynamic effect that closely parallels equilibrium temperature chaos. This dynamic temperature-chaos effect is spatially heterogeneous to a large degree and turns out to be controlled by the spin-glass coherence length ξ. Indeed, an emerging length-scale ξ* rules the crossover from weak (at ξ ≪ ξ*) to strong chaos (ξ ≫ ξ*). Extrapolations of ξ* to relevant experimental conditions are provided.
Next-generation battery research will heavily rely on physico-chemical models, combined with deep learning methods and high-throughput and quantitative analysis of experimental datasets, encoding spectral information in space and time. These tasks will require highly efficient computational approaches, to yield rapidly accurate approximations of the models. This paper explores the capabilities of a representative range of model reduction techniques to face this problem in the case of a well-assessed electrochemical phase-formation model. We consider the Proper Orthogonal Decomposition (POD) with a Galerkin projection and the Dynamic Mode Decomposition (DMD) techniques to deal first of all with a semi-linear heat equation 2D in space as a test problem. As an application, we show that it is possible to save computational time by applying POD-Galerkin for different choices of the parameters without recalculating the snapshot matrix. Finally, we consider two reaction–diffusion (RD) PDE systems with Turing-type dynamics: the well-known Schnackenberg model and the DIB model for electrochemical phase formation. We show that their reduced models obtained by POD and DMD with suitable low-dimensional projections are able to approximate carefully both the Turing patterns at the steady state and the reactivity dynamics in the transient regime. Finally, for the DIB model we show that POD-Galerkin applied for different choices of parameters, by calculating once the snapshot matrices, is able to find reduced Turing patterns of different morphology.
Battery modelling
Dynamic Mode Decomposition
Model Order Reduction (MOR)
POD-Galerkin
Reaction–diffusion PDE systems
Turing patterns
Cherenkov probes and runaway electrons diagnostics
Kwiatkowski R.
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Rabinski M.
;
Sadowski M. J.
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Zebrowski J.
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Karpinski P.
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Coda S.
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Agostini M.
;
Albanese R.
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Alberti S.
;
Alessi E.
;
Allan S.
;
Allcock J.
;
Ambrosino R.
;
Anand H.
;
Andrebe Y.
;
Arnichand H.
;
Auriemma F.
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Ayllon-Guerola J. M.
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Bagnato F.
;
Ball J.
;
Baquero-Ruiz M.
;
Beletskii A. A.
;
Bernert M.
;
Bin W.
;
Blanchard P.
;
Blanken T. C.
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Boedo J. A.
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Bogar O.
;
Bolzonella T.
;
Bombarda F.
;
Bonanomi N.
;
Bouquey F.
;
Bowman C.
;
Brida D.
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Bucalossi J.
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Buermans J.
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Bufferand H.
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Buratti P.
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Calabro G.
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Calacci L.
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Camenen Y.
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Carnevale D.
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Carpanese F.
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Carr M.
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Carraro L.
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Casolari A.
;
Causa F.
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Cerovsky J.
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Chellai O.
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Chmielewski P.
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Choi D.
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Christen N.
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Ciraolo G.
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Cordaro L.
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Costea S.
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Cruz N.
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Czarnecka A.
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Molin A. D.
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David P.
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Decker J.
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De Oliveira H.
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Douai D.
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Dreval M. B.
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Dudson B.
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Dunne M.
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Duval B. P.
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Eich T.
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Elmore S.
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Embreus O.
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Esposito B.
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Faitsch M.
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Farnik M.
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Fasoli A.
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Fedorczak N.
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Felici F.
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Feng S.
;
Feng X.
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Ferro G.
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Fevrier O.
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Ficker O.
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Fil A.
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Fontana M.
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Frassinetti L.
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Furno I.
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Gahle D. S.
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Galassi D.
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Galazka K.
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Gallo A.
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Galperti C.
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Garavaglia S.
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Garcia J.
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Garcia-Munoz M.
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Garrido A. J.
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Garrido I.
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Gath J.
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Geiger B.
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Giruzzi G.
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Gobbin M.
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Goodman T. P.
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Gorini G.
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Gospodarczyk M.
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Granucci G.
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Graves J. P.
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Gruca M.
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Gyergyek T.
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Hakola A.
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Happel T.
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Harrer G. F.
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Harrison J.
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Havlickova E.
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Hawke J.
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Henderson S.
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Hennequin P.
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Hesslow L.
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Hogeweij D.
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Hogge J. -P.
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Hopf C.
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Hoppe M.
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Horacek J.
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Huang Z.
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Hubbard A.
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Iantchenko A.
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Igochine V.
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Innocente P.
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Schrittwieser C. I.
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Isliker H.
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Jacquier R.
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Jardin A.
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Kappatou A.
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Karpushov A.
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Kazantzidis P. -V.
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Keeling D.
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Kirneva N.
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Komm M.
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Kong M.
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Kovacic J.
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Krawczyk N.
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Kudlacek O.
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Kurki-Suonio T.
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Kwiatkowski R.
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Labit B.
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Lazzaro E.
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Linehan B.
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Lipschultz B.
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Llobet X.
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Lombroni R.
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Loschiavo V. P.
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Lunt T.
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Macusova E.
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Madsen J.
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Maljaars E.
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Mantica P.
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Maraschek M.
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Marchetto C.
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Marco A.
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Mariani A.
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Marini C.
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Martin Y.
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Matos F.
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Maurizio R.
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Mavkov B.
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Mazon D.
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McCarthy P.
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McDermott R.
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Menkovski V.
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Merle A.
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Meyer H.
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Micheletti D.
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Militello F.
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Mitosinkova K.
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Mlynar J.
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Moiseenko V.
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Cabrera P. A. M.
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Morales J.
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Moret J. -M.
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Moro A.
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Mumgaard R. T.
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Naulin V.
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Nem R. D.
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Nespoli F.
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Nielsen A. H.
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Nielsen S. K.
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Nocente M.
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Nowak S.
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Offeddu N.
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Orsitto F. P.
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Paccagnella R.
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Palha A.
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Papp G.
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Pau A.
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Pavlichenko R. O.
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Perek A.
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Pericoli Ridolfini V.
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Pesamosca F.
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Piergotti V.
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Pigatto L.
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Piovesan P.
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Piron C.
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Plyusnin V.
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Poli E.
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Porte L.
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Pucella G.
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Puiatti M. E.
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Putterich T.
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Rasmussen J. J.
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Ravensbergen T.
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Reich M.
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Reimerdes H.
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Reimold F.
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Reux C.
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Ricci D.
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Ricci P.
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Rispoli N.
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Rosato J.
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Saarelma S.
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Salewski M.
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Salmi A.
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Sauter O.
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Scheffer M.
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Schlatter C.
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Schneider B. S.
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Schrittwieser R.
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Sharapov S.
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Sheeba R. R.
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Sheikh U.
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Shousha R.
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Silva M.
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Sinha J.
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Sozzi C.
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Spolaore M.
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Stipani L.
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Strand P.
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Tala T.
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Biwole A. S. T.
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Teplukhina A. A.
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Testa D.
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Theiler C.
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Thornton A.
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Tomaz G.
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Tomes M.
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Tran M. Q.
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Tsironis C.
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Tsui C. K.
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Urban J.
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Valisa M.
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Vallar M.
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Van Vugt D.
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Vartanian S.
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Vasilovici O.
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Verhaegh K.
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Vermare L.
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Vianello N.
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Viezzer E.
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Vijvers W. A. J.
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Villone F.
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Voitsekhovitch I.
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Vu N. M. T.
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Walkden N.
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Wauters T.
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Weiland M.
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Weisen H.
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Wensing M.
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Wiesenberger M.
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Wilkie G.
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Wischmeier M.
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Wu K.
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Yoshida M.
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Zagorski R.
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Zanca P.
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Zisis A.
;
Zuin M.
The beams of fast runaway electrons (RE), which are often produced during tokamak discharges, are particularly dangerous and can induce serious damages of the vacuum vessel and internal components of the machine. The proper and fast diagnostics of RE beams is essential for controlling the discharge, e.g., by early mitigation of disruptions and potentially dangerous RE beams. The diagnostics of RE beams is usually based on measurements of the radiation emitted either by these electrons, or as a result of their interactions with plasma and/or vessel walls. Such a radiation is usually recorded by the means of probes placed outside the vacuum vessel. The method developed by our team is based on the probe located inside the vacuum vessel. The probe can be used to detect highly localized RE bunches and to determine their spatial and temporal characteristics. During last few years, the NCBJ team have developed and used the RE diagnostics based on the Cherenkov effect observed in diamond radiators coupled with fast photomultipliers. During the investigated discharges, the probe was inserted into the vacuum vessel, and its head was placed at the plasma edge, where fast RE are expected. A correlation between signals recorded using our probes and other diagnostics, e.g., hard x-ray signals, was also studied. In this paper, we present recent results of the RE measurements by means of Cherenkov probes, which were performed in the COMPASS and TCV tokamaks.
Exposure of Von Willebrand Factor Cleavage Site in A1A2A3-Fragment under Extreme Hydrodynamic Shear
Olivier Languin-Cattoën
;
Emeline Laborie
;
Daria O. Yurkova
;
Simone Melchionna
;
Philippe Derreumaux
;
Aleksey V. Belyaev
;
Fabio Sterpone
Abstract Von Willebrand Factor (vWf) is a giant multimeric extracellular blood plasma involved in hemostasis. In this work we present multi-scale simulations of its three-domains fragment A1A2A3. These three domains are essential for the functional regulation of vWf. Namely the A2 domain hosts the site where the protease ADAMTS13 cleavages the multimeric vWf allowing for its length control that prevents thrombotic conditions. The exposure of the cleavage site follows the elongation/unfolding of the domain that is caused by an increased shear stress in blood. By deploying Lattice Boltzmann molecular dynamics simulations based on the OPEP coarse-grained model for proteins, we investigated at molecular level the unfolding of the A2 domain under the action of a perturbing shear flow. We described the structural steps of this unfolding that mainly concerns the beta-strand structures of the domain, and we compared the process occurring under shear with that produced by the action of a directional pulling force, a typical condition of single molecule experiments. We observe, that under the action of shear flow, the competition among the elongational and rotational components of the fluid field leads to a complex behaviour of the domain, where elongated structures can be followed by partially collapsed melted globule structures with a very different degree of exposure of the cleavage site. Our simulations pose the base for the development of a multi-scale in-silico description of vWf dynamics and functionality in physiological conditions, including high resolution details for molecular relevant events, e.g., the binding to platelets and collagen during coagulation or thrombosis.
We present a numerical investigation of the airflow dynamics and particle transport through an averaged human nasal cavity. The effect of particle size and breathing rate on the deposition patterns are explored. The simulations reveal that smaller particles penetrate deeper into the airway, whereas larger particles agglomerate near the anterior portion of the nasal cavity. Increasing the flow rate augmented the penetration of the particles. The complex interplay of the finite particle size and the flow inertia decided the spatial deposition of the particles. The findings from this study demonstrate the efficacy of state-of-art simulation frameworks for targeting respiratory disorders.
The societal impact of traffic is a long-standing and complex problem. We focus on the estimation of ground-level ozone production due to vehicular traffic. We propose a comprehensive computational approach combining four consecutive modules: a traffic simulation module, an emission module, a module for the main chemical reactions leading to ozone production, and a module for the diffusion of gases in the atmosphere. The traffic module is based on a second-order traffic flow model, obtained by choosing a special velocity function for the Collapsed Generalized Aw-Rascle-Zhang model. A general emission module is taken from literature, and tuned on NGSIM data together with the traffic module. Last two modules are based on reaction-diffusion partial differential equations. The system of partial differential equations describing the main chemical reactions of nitrogen oxides presents a source term given by the general emission module applied to the output of the traffic module. We use the proposed approach to analyze the ozone impact of various traffic scenarios and describe the effect of traffic light timing. The numerical tests show the negative effect of vehicles restarts on emissions, and the consequent increase in pollutants in the air, suggesting to increase the length of the green phase of traffic lights.
road traffic modeling; second-order traffic models; emissions; ozone production
In order to solve Prandtl--type equations we propose a collocation--quadrature method based on de la Vallée Poussin (briefly VP) filtered interpolation at Chebyshev nodes. Uniform convergence and stability are proved in a couple of Holder--Zygmund spaces of locally continuous functions. With respect to classical methods based on Lagrange interpolation at the same collocation nodes, we succeed in reproducing the optimal convergence rates of the L2 case and cut off the typical log factor which seemed inevitable dealing with uniform norms. Such an improvement does not require a greater computational effort. In particular, we propose a fast algorithm based on the solution of a simple 2-bandwidth linear system and prove that, as its dimension tends to infinity, the sequence of the condition numbers (in any natural matrix norm) tends to a finite limit.
Prandtl equation
Hypersingular integral equations
Polynomial interpolation
Filtered approximation
De la Vallée Poussin mean
Holder-Zygmund spaces
Chebyshev nodes
The optimal Orlicz target space is exhibited for embeddings of fractional-order Orlicz-Sobolev spaces in $R^n$. An improved embedding with an Orlicz-Lorentz target space, which is optimal in the broader class of all rearrangement-invariant spaces, is also established. Both spaces of order s in (0, 1), and higher-order spaces are considered. Related Hardy type inequalities are proposed as well.
Some recent results on the theory of fractional Orlicz-Sobolev spaces are surveyed. They concernSobolev type embeddings for these spaces with an optimal Orlicz target, related Hardy type inequalities, andcriteria for compact embeddings. The limits of these spaces when the smoothness parameter s in (0, 1) tendsto either of the endpoints of its range are also discussed. This note is based on the papers [1, 2, 3, 4], whereadditional material and proofs can be found.
Short-Term Load Forecasting (STLF) is a fundamental instrument in the efficient operational management and planning of electric utilities. Emerging smart grid technologies pose new challenges and opportunities. Although load forecasting at the aggregate level has been extensively studied, electrical load forecasting at fine-grained geographical scales of households is more challenging. Among existing approaches, semi-parametric generalized additive models (GAM) have been increasingly popular due to their accuracy, flexibility, and interpretability. Their applicability is justified when forecasting is addressed at higher levels of aggregation, since the aggregated load pattern contains relatively smooth additive components. High resolution data are highly volatile, forecasting the average load using GAM models with smooth components does not provide meaningful information about the future demand. Instead, we need to incorporate irregular and volatile effects to enhance the forecast accuracy. We focus on the analysis of such hybrid additive models applied on smart meters data and show that it leads to improvement of the forecasting performances of classical additive models at low aggregation levels. (C) 2020 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.
Short-term load forecasting
Semi-parametric additive model
Random forest
Wavelets
Penalised least-squares
We investigate the rheology of strain-hardening spherical capsules, from the dilute tothe concentrated regime under a confined shear flow using three-dimensional numericalsimulations. We consider the effect of capillary number, volume fraction and membrane inextensibility on the particle deformation and on the effective suspension viscosity andnormal stress differences of the suspension. The suspension displays a shear-thinningbehaviour that is a characteristic of soft particles such as emulsion droplets, vesicles,strain-softening capsules and red blood cells. We find that the membrane inextensibilityplays a significant role on the rheology and can almost suppress the shear-thinning. Forconcentrated suspensions a non-monotonic dependence of the normal stress differenceson the membrane inextensibility is observed, reflecting a similar behaviour in the particleshape. The effective suspension viscosity, instead, grows and eventually saturates, for verylarge inextensibilities, approaching the solid particle limit. In essence, our results revealthat strain-hardening capsules share rheological features with both soft and solid particlesdepending on the ratio of the area dilatation to shear elastic modulus. Furthermore, thesuspension viscosity exhibits a universal behaviour for the parameter space defined by the capillary number and the membrane inextensibility, when introducing the particlegeometrical changes at the steady state in the definition of the volume fraction.
Soft Matter
Rheology
Capsules
Theory of elasticity
Numerical simulations
