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This study investigated chemical composition, cytotoxicity in normal and cancer cells, and antimicrobial and antioxidant activity of the essential oil (EO) isolated by hydrodistillation from the discarded leaves of lemon (Citrus limon) plants cultivated in Sardinia (Italy). The volatile chemical composition of lemon leaf EO (LLEO) was analyzed with gas chromatography-mass spectrometry combined with flame ionization detection (GC/MS and GC/FID). The most abundant component of LLEO was limonene (260.7 mg/mL), followed by geranial (102.6 mg/mL) and neral (88.3 mg/mL). The antimicrobial activity of LLEO was tested using eight bacterial strains and two types of yeasts by a microdilution broth test. Candida albicans showed the greatest susceptibility (MIC = 0.625 μL/mL) and Listeria monocytogenes and Staphylococcus aureus were inhibited at low LLEO concentration (MIC values from 2.5 to 5 μL/mL). The C. limon leaf EO displayed radical scavenging ability (IC50 value of 10.24 mg/mL) in the 2,2-diphenyl-1-picryl-hydrazylhydrate (DPPH) assay. Furthermore, the LLEO impact on cell viability was explored by 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide (MTT) assay in cancer HeLa cells, A375 melanoma cell line, normal fibroblasts (3T3 cells), and keratinocytes (HaCaT cells). LLEO, at 24 h of incubation, significantly reduced viability from 25 μM in Hela cells (33% reduction) and A375 cells (27%), greatly affecting cell morphology, whereas this effect was found from 50 μM on 3T3 fibroblasts and keratinocytes. LLEO’s pro-oxidant effect was also established in HeLa cells by 2′,7′-dichlorodihydrofluorescein diacetate assay.

To evaluate whether postoperative serum hyperamylasemia (POH), with drain fluid amylase (DFA) and C-reactive protein (CRP), improves the Fistula Risk Score (FRS) accuracy in assessing the risk of a postoperative pancreatic fistula (POPF).The FRS predicts POPF occurrence using intraoperative predictors with good accuracy but intrinsic limits.Outcomes of patients who underwent pancreaticoduodenectomies (PD) between 2016 and 2021 were evaluated across FRS risk zones and POH occurrence. POH consists of serum amylase activity greater than the upper limit of normal (52 U/l), persisting within the first 48 hours postoperatively (postoperative day -POD- 1 and 2).Out of 905 PDs, some FRS elements, namely soft pancreatic texture (OR 11.6), pancreatic duct diameter (OR 0.80), high-risk pathological diagnosis (OR 1.54), but not higher blood loss (OR 0.99), were associated with POH. POH was an independent predictor of POPF, which occurred in 46.8% of POH cases (P0.001). Once POH occurs, POPF incidence rises from 3.8% to 42.9%, 22.9% to 41.7%, and 48.9% to 59.2% in patients intraoperatively classified at low, moderate and high FRS risk, respectively. The predictive ability of multivariable models adding POD 1 drain fluid amylase, POD 1-2 POH and POD 3 C-reactive protein to the FRS showed progressively and significantly higher accuracy (AUC FRS=0.82, AUC FRS-DFA=0.85, AUC FRS-DFA-POH=0.87, AUC FRS-DFA-POH-CRP=0.90, DeLong always P0.05).POPF risk assessment should follow a dynamic process. The stepwise retrieval of early, postoperative biologic markers improves clinical risk stratification by increasing the granularity of POPF risk estimates and affords a possible therapeutic window before the actual morbidity of POPF occurs.

In this work we present an extension of the Virtual Element Method with curved edges for the numerical approximation of the second order wave equation in a bidimensional setting. Curved elements are used to describe the domain boundary, as well as internal interfaces corresponding to the change of some mechanical parameters. As opposite to the classic and isoparametric Finite Element approaches, where the geometry of the domain is approximated respectively by piecewise straight lines and by higher order polynomial maps, in the proposed method the geometry is exactly represented, thus ensuring a highly accurate numerical solution. Indeed, if in the former approach the geometrical error might deteriorate the quality of the numerical solution, in the latter approach the curved interfaces/boundaries are approximated exactly guaranteeing the expected order of convergence for the numerical scheme. Theoretical results and numerical findings confirm the validity of the proposed approach.

In this study, we propose a virtual element scheme to solve the Darcy problem in three physical dimensions. The main novelty is that curved elements are naturally handled without any degradation of the solution accuracy. Indeed, in presence of curved boundaries, or internal interfaces, the geometrical error introduced by planar approximations may dominate the convergence rate limiting the benefit of high-order approximations. We consider the Darcy problem in its mixed form to directly obtain accurate and mass conservative fluxes without any post-processing. An important step to derive the proposed scheme is the integration over curved polyhedrons, here presented and discussed. Finally, we show the theoretical analysis of the scheme as well as several numerical examples to support our findings.

We consider the \begin{document}$ C^1 $\end{document}-Virtual Element Method (VEM) for the conforming numerical approximation of some variants of the Cahn-Hilliard equation on polygonal meshes. In particular, we focus on the discretization of the advective Cahn-Hilliard problem and the Cahn-Hilliard inpainting problem. We present the numerical approximation and several numerical results to assess the efficacy of the proposed methodology. Correction: Bari is added after the zip code 70125 in third author’s address. We apologize for any inconvenience this may cause.

Evaluation of cosmic ray trajectories and penetration inside the Earth environment is mandatory for estimation of flux by on-orbit detectors as well as of radiation damage on electronics devices and biological tissues, like those of astronauts onboard the International Space Station. We studied the impact of the external magnetic field on the calculation of some parameters like the rigidity cut-off, by a quantitative comparison among several geomagnetic field models. For this purpose we used GeoMagSphere back-tracing code, performing the particle trajectory reconstruction back-in-time from the chosen position and time up to the borders of the magnetosphere. The analysis done points out the need to combine an external magnetic field model with the internal one (usually IGRF). Several external field models have a different impact on the accuracy as well as on the time needed for calculation, important in case of a large amount of back-traced particles. We also studied cosmic ray propagation inside the magnetosphere, separately for quiet and disturbed solar activity periods. We found that during highly disturbed periods and during magnetic storms, rigidity cut-off, as well as cosmic ray flux, can be appropriately evaluated only by using external field models, like that one proposed by Tsyganenko and Sitnov (2005), well describing those particular conditions.

In this paper, we extend the divergence-free VEM of [L. Beirão da Veiga, C. Lovadina and G. Vacca, Virtual elements for the Navier–Stokes problem on polygonal meshes, SIAM J. Numer. Anal. 56 (2018) 1210–1242] to the Oseen problem, including a suitable stabilization procedure that guarantees robustness in the convection-dominated case without disrupting the divergence-free property. The stabilization is inspired from [N. Ahmed, G. R. Barrenechea, E. Burman, J. Guzman, A. Linke and C. Merdon, A pressure-robust discretization of Oseen’s equation using stabilization in the vorticity equation, SIAM J. Numer. Anal. 59 (2021) 2746–2774] and includes local SUPG-like terms of the vorticity equation, internal jump terms for the velocity gradients, and an additional VEM stabilization. We derive theoretical convergence results that underline the robustness of the scheme in different regimes, including the convection-dominated case. Furthermore, as in the non-stabilized case, the influence of the pressure on the velocity error is moderate, as it appears only through higher-order terms.

The objective of this contribution is to develop a convergence analysis for SUPG-stabilized Virtual Element Methods in diffusion-convection problems that is robust also in the convection dominated regime. For the original method introduced in [Benedetto et al., CMAME 2016] we are able to show an “almost uniform” error bound (in the sense that the unique term that depends in an unfavourable way on the parameters is damped by a higher order mesh-size multiplicative factor). We also introduce a novel discretization of the convection term that allows us to develop error estimates that are fully robust in the convection dominated cases. We finally present some numerical result.

In this work, we propose an extension of the mixed Virtual Element Method (VEM) for bi-dimensional computational grids with curvilinear edge elements. The approximation by means of rectilinear edges of a domain with curvilinear geometrical feature, such as a portion of domain boundary or an internal interface , may introduce a geometrical error that degrades the expected order of convergence of the scheme. In the present work a suitable VEM approximation space is proposed to consistently handle curvilinear geometrical objects, thus recovering optimal convergence rates. The resulting numerical scheme is presented along with its theoretical analysis and several numerical test cases to validate the proposed approach.

In the present paper, we investigate the underlying Stokes complex structure of the Virtual Element Method for Stokes and Navier–Stokes introduced in previous papers by the same authors, restricting our attention to the two dimensional case. We introduce a Virtual Element space $${\varPhi }_h \subset H^2({\varOmega })$$ Φ h ⊂ H 2 ( Ω ) and prove that the triad $$\{{\varPhi }_h, {\varvec{V}}_h, Q_h\}$$ { Φ h , V h , Q h } (with $${\varvec{V}}_h$$ V h and $$Q_h$$ Q h denoting the discrete velocity and pressure spaces) is an exact Stokes complex. Furthermore, we show the computability of the associated differential operators in terms of the adopted degrees of freedom and explore also a different discretization of the convective trilinear form. The theoretical findings are supported by numerical tests.

We present the essential tools to deal with virtual element method (VEM) for the approximation of solutions of partial differential equations in mixed form. Functional spaces, degrees of freedom, projectors and differential operators are described emphasizing how to build them in a virtual element framework and for a general approximation order. To achieve this goal, it was necessary to make a deep analysis on polynomial spaces and decompositions. We exploit such “bricks” to construct virtual element approximations of Stokes, Darcy and Navier–Stokes problems and we provide a series of examples to numerically verify the theoretical behaviour of high-order VEM.

The focus of this paper is on developing a virtual element method (VEM) for Darcy and Brinkman equations. In [L. Beirão da Veiga, C. Lovadina and G. Vacca, ESAIM Math. Model. Numer. Anal. 51 (2017)], we presented a family of virtual elements for Stokes equations and we defined a new virtual element space of velocities such that the associated discrete kernel is pointwise divergence-free. We use a slightly different virtual element space having two fundamental properties: the [Formula: see text]-projection onto [Formula: see text] is exactly computable on the basis of the degrees of freedom, and the associated discrete kernel is still pointwise divergence-free. The resulting numerical scheme for the Darcy equation has optimal order of convergence and [Formula: see text]-conforming velocity solution. We can apply the same approach to develop a robust virtual element method for the Brinkman equation that is stable for both the Stokes and Darcy limit case. We provide a rigorous error analysis of the method and several numerical tests.

We study the virtual element approximation of elliptic eigenvalue problems. The main result of the article states that the virtual element method provides an optimal-order approximation of the eigenmodes. A wide set of numerical tests confirm the theoretical analysis

In the present paper we develop the Virtual Element Method for hyperbolic problems on polygonal meshes, considering the linear wave equations as our model problem. After presenting the semi-discrete scheme, we derive the convergence estimates in H^1 semi-norm and L^2 norm. Moreover we develop a theoretical analysis on the stability for the fully discrete problem by comparing the Newmark method and the Bathe method. Finally we show the practical behaviour of the proposed method through a large array of numerical tests.

The Mimetic Finite Difference (MFD) methods for PDEs mimic crucial properties of mathematical systems: duality and self-adjointness of differential operators, conservation laws and properties of the solution on general polytopal meshes. In this article the structure and the spectral properties of the linear systems derived by the spatial discretization of diffusion problem are analysed. In addition, the numerical approximation of parabolic equations is discussed where the MFD approach is used in the space discretization while implicit ? -method and explicit Runge-Kutta-Chebyshev schemes are used in time discretization. Moreover, we will show how the numerical solution preserves certain conservation laws of the theoretical solution.

In the present paper we develop a new family of Virtual Elements for the Stokes problem on polygonal meshes. By a proper choice of the Virtual space of velocities and the associated degrees of freedom, we can guarantee that the final discrete velocity is pointwise divergence-free, and not only in a relaxed (projected) sense, as it happens for more standard elements. Moreover, we show that the discrete problem is immediately equivalent to a reduced problem with fewer degrees of freedom, thus yielding a very efficient scheme. We provide a rigorous error analysis of the method and several numerical tests, including a comparison with a different Virtual Element choice.

We assume the DE state equations w(a) = w_0+w_a(a_p-a), and study the dependence of the constraints on w_0 and w_a coefficients on the pivoting redshift 1+z_p=1/a_p. Coefficients are fitted to data including WMAP7, SNIa (Union 2.1), BAO's (including WiggleZ and SDSS results) and H_0 constraints. The fitting algorithm is CosmoMC. We find specific differences between the cases when neutrino mass is allowed or disregarded. More in detail: i) The z_p value yielding uncorrelated constraints on w_0 and w_a is different in the two cases, holding ~0.25 and ~0.35, respectively. (ii) If we consider the intervals allowed to w_0, we find that they shift when z_p increases, in opposite directions for vanishing or allowed neutrino mass. This leads to no overlap between 1sigma intervals already at z_p >~0.4. (iii) The known effect that a more negative state parameter is required to allow for neutrino mass displays its effects on w_a, rather than on w_0. (iv) The w_0-w_a constraints found by using any pivot z_p can be translated into constraints holding at a specific z_p value (0 or the z_p where errors are uncorrelated). When we do so, error ellipses exhibit a satisfactory overlap., 13 pages, 7 figures, 2 tables

When cosmic microwave background data are used to derive cosmological parameters, their very choice does matter: some parameter values can be biased if the parameter space does not cover the "true" model. This is a problem because of the difficulty in parameterizing dark energy (DE) physics. We test this risk through numerical experiments. We create artificial data for dynamical or coupled DE models and then use Monte Carlo Markov Chain techniques to recover model parameters by assuming a constant DE state parameter w and no DM-DE coupling. For the DE potential considered, no serious bias arises when coupling is absent. In contrast, ωo,c and thence Ho and Ωo,m suffer a serious bias when the "true" cosmology includes even just a mild DM-DE coupling. Until the nature of the dark components remains unknown, it can be important to allow for a degree of freedom accounting for DM-DE coupling, even more than increasing the number of parameters accounting for the w(a) behavior. © 2009. The American Astronomical Society. All rights reserved.

In this paper we initiate the investigation of Virtual Elements with curved faces. We consider the case of a fixed curved boundary in two dimensions, as it happens in the approximation of problems posed on a curved domain or with a curved interface. While an approximation of the domain with polygons leads, for degree of accuracy k≥2, to a sub-optimal rate of convergence, we show (both theoretically and numerically) that the proposed curved VEM lead to an optimal rate of convergence.