We present a model for the fast evaluation of the total drag of ship hulls operating in both wet and dry transom stern conditions, in calm or wavy water, based on the combination of an unsteady semi-Lagrangian potential flow formulation with fully nonlinear free-surface treatment, experimental correlations, and simplified viscous drag modeling. The implementation is entirely based on open source libraries. The spatial discretization is solved using a streamline upwind Petrov‐Galerkin stabilization of an iso-parametric, collocation based, boundary element method, implemented using the open source library deal.II. The resulting nonlinear differential-algebraic system is integrated in time using implicit backward differentiation formulas, implemented in the open source library SUNDIALS. The Open CASCADE library is used to interface the model directly with computer-aided design data structures. The model accounts automatically for hulls with a transom stern, both in wet and dry regimes, by using a specific treatment of the free-surface nodes on the stern edge that automatically detects when the hull advances at low speeds. In this case, the transom stern is partially immersed, and a pressure patch is applied on the water surface detaching from the transom stern, to recover the gravity effect of the recirculating water on the underlying irrotational flow domain. The parameters of the model used to impose the pressure patch are approximated from experimental relations found in the literature. The test cases considered are those of the U.S. Navy Combatant DTMB-5415 and the National Physical Laboratory hull. Comparisons with experimental data on quasi-steady test cases for both water elevation and total hull drag are presented and discussed. The quality of the results obtained on quasi-steady simulations suggests that this model can represent a promising alternative to current unsteady solvers for simulations with Froude numbers below 0.35.

VL - 61 ER - TY - RPRT T1 - The wave equation on domains with cracks growing on a prescribed path: existence, uniqueness, and continuous dependence on the data Y1 - 2015 A1 - Gianni Dal Maso A1 - Ilaria Lucardesi AB - Given a bounded open set $\Omega \subset \mathbb R^d$ with Lipschitz boundary and an increasing family $\Gamma_t$, $t\in [0,T]$, of closed subsets of $\Omega$, we analyze the scalar wave equation $\ddot{u} - div (A \nabla u) = f$ in the time varying cracked domains $\Omega\setminus\Gamma_t$. Here we assume that the sets $\Gamma_t$ are contained into a prescribed $(d-1)$-manifold of class $C^2$. Our approach relies on a change of variables: recasting the problem on the reference configuration $\Omega\setminus \Gamma_0$, we are led to consider a hyperbolic problem of the form $\ddot{v} - div (B\nabla v) + a \cdot \nabla v - 2 b \cdot \nabla \dot{v} = g$ in $\Omega \setminus \Gamma_0$. Under suitable assumptions on the regularity of the change of variables that transforms $\Omega\setminus \Gamma_t$ into $\Omega\setminus \Gamma_0$, we prove existence and uniqueness of weak solutions for both formulations. Moreover, we provide an energy equality, which gives, as a by-product, the continuous dependence of the solutions with respect to the cracks. UR - http://urania.sissa.it/xmlui/handle/1963/34629 U1 - 34832 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - A weighted empirical interpolation method: A priori convergence analysis and applications Y1 - 2014 A1 - Peng Chen A1 - Alfio Quarteroni A1 - Gianluigi Rozza AB - We extend the classical empirical interpolation method [M. Barrault, Y. Maday, N.C. Nguyen and A.T. Patera, An empirical interpolation method: application to efficient reduced-basis discretization of partial differential equations. Compt. Rend. Math. Anal. Num. 339 (2004) 667-672] to a weighted empirical interpolation method in order to approximate nonlinear parametric functions with weighted parameters, e.g. random variables obeying various probability distributions. A priori convergence analysis is provided for the proposed method and the error bound by Kolmogorov N-width is improved from the recent work [Y. Maday, N.C. Nguyen, A.T. Patera and G.S.H. Pau, A general, multipurpose interpolation procedure: the magic points. Commun. Pure Appl. Anal. 8 (2009) 383-404]. We apply our method to geometric Brownian motion, exponential Karhunen-Loève expansion and reduced basis approximation of non-affine stochastic elliptic equations. We demonstrate its improved accuracy and efficiency over the empirical interpolation method, as well as sparse grid stochastic collocation method. PB - EDP Sciences UR - http://urania.sissa.it/xmlui/handle/1963/35021 U1 - 35253 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Weighted quantile correlation test for the logistic family Y1 - 2014 A1 - Ferenc Balogh A1 - Éva Krauczi AB - We summarize the results of investigating the asymptotic behavior of the weighted quantile correlation tests for the location-scale family associated to the logistic distribution. Explicit representations of the limiting distribution are given in terms of integrals of weighted Brownian bridges or alternatively as infinite series of independent Gaussian random variables. The power of this test and the test for the location logistic family against some alternatives are demonstrated by numerical simulations. PB - University of Szeged UR - http://urania.sissa.it/xmlui/handle/1963/35025 U1 - 35261 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - Where best to place a Dirichlet condition in an anisotropic membrane? Y1 - 2014 A1 - Paolo Tilli A1 - Davide Zucco AB - We study a shape optimization problem for the first eigenvalue of an elliptic operator in divergence form, with non constant coefficients, over a fixed domain $\Omega$. Dirichlet conditions are imposed along $\partial\Omega$ and, in addition, along a set $\Sigma$ of prescribed length ($1$-dimensional Hausdorff measure). We look for the best shape and position for the supplementary Dirichlet region $\Sigma$ in order to maximize the first eigenvalue. We characterize the limit distribution of the optimal sets, as their prescribed length tends to infinity, via $\Gamma$-convergence. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/7481 U1 - 7592 ER - TY - JOUR T1 - A weighted reduced basis method for elliptic partial differential equations with random input data JF - SIAM Journal on Numerical Analysis Y1 - 2013 A1 - Peng Chen A1 - Alfio Quarteroni A1 - Gianluigi Rozza AB - In this work we propose and analyze a weighted reduced basis method to solve elliptic partial differential equations (PDEs) with random input data. The PDEs are first transformed into a weighted parametric elliptic problem depending on a finite number of parameters. Distinctive importance of the solution at different values of the parameters is taken into account by assigning different weights to the samples in the greedy sampling procedure. A priori convergence analysis is carried out by constructive approximation of the exact solution with respect to the weighted parameters. Numerical examples are provided for the assessment of the advantages of the proposed method over the reduced basis method and the stochastic collocation method in both univariate and multivariate stochastic problems. VL - 51 ER - TY - JOUR T1 - Weighted barycentric sets and singular Liouville equations on compact surfaces JF - Journal of Functional Analysis 262 (2012) 409-450 Y1 - 2012 A1 - Alessandro Carlotto A1 - Andrea Malchiodi AB - Given a closed two dimensional manifold, we prove a general existence result\\r\\nfor a class of elliptic PDEs with exponential nonlinearities and negative Dirac\\r\\ndeltas on the right-hand side, extending a theory recently obtained for the\\r\\nregular case. This is done by global methods: since the associated Euler\\r\\nfunctional is in general unbounded from below, we need to define a new model\\r\\nspace, generalizing the so-called space of formal barycenters and\\r\\ncharacterizing (up to homotopy equivalence) its very low sublevels. As a\\r\\nresult, the analytic problem is reduced to a topological one concerning the\\r\\ncontractibility of this model space. To this aim, we prove a new functional\\r\\ninequality in the spirit of [16] and then we employ a min-max scheme based on a cone-style construction, jointly with the blow-up analysis given in [5] (after\\r\\n[6] and [8]). This study is motivated by abelian Chern- Simons theory in\\r\\nself-dual regime, or from the problem of prescribing the Gaussian curvature in\\r\\npresence of conical singularities (hence generalizing a problem raised by\\r\\nKazdan and Warner in [26]). PB - Elsevier UR - http://hdl.handle.net/1963/5218 U1 - 5040 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Wild quiver gauge theories JF - JHEP 02(2012)031 Y1 - 2012 A1 - Giulio Bonelli A1 - Kazunobu Maruyoshi A1 - Alessandro Tanzini AB -We study $N=2$ supersymmetric $SU(2)$ gauge theories coupled to non-Lagrangian superconformal field theories induced by compactifying the six dimensional $A_1 (2,0)$ theory on Riemann surfaces with irregular punctures. These are naturally associated to Hitchin systems with wild ramification whose spectral curves provide the relevant Seiberg-Witten geometries. We propose that the prepotential of these gauge theories on the Omega-background can be obtained from the corresponding irregular conformal blocks on the Riemann surfaces via a generalization of the coherent state construction to the case of higher order singularities.

PB - SISSA UR - http://hdl.handle.net/1963/5184 N1 - 34 pages U1 - 4999 U2 - Physics U3 - Elementary Particle Theory U4 - -1 ER - TY - JOUR T1 - The well-posedness issue for the density-dependent Euler equations in endpoint Besov spaces JF - Journal de Mathématiques Pures et Appliquées Y1 - 2011 A1 - Raphaël Danchin A1 - Francesco Fanelli KW - Blow-up criterion KW - Critical regularity KW - Incompressible Euler equations KW - Lifespan KW - Nonhomogeneous inviscid fluids AB -This work is the continuation of the recent paper (Danchin, 2010) [9] devoted to the density-dependent incompressible Euler equations. Here we concentrate on the well-posedness issue in Besov spaces of type B∞,rs embedded in the set of Lipschitz continuous functions, a functional framework which contains the particular case of Hölder spaces C1,α and of the endpoint Besov space B∞,11. For such data and under the non-vacuum assumption, we establish the local well-posedness and a continuation criterion in the spirit of that of Beale, Kato and Majda (1984) [2]. In the last part of the paper, we give lower bounds for the lifespan of a solution. In dimension two, we point out that the lifespan tends to infinity when the initial density tends to be a constant. This is, to our knowledge, the first result of this kind for the density-dependent incompressible Euler equations. Résumé Ce travail complète lʼarticle récent (Danchin, 2010) [9] consacré au système dʼEuler incompressible à densité variable. Lorsque lʼétat initial ne comporte pas de vide, on montre ici que le système est bien posé dans tous les espaces de Besov B∞,rs inclus dans lʼensemble des fonctions lipschitziennes. Ce cadre fonctionnel contient en particulier les espaces de Hölder C1,α et lʼespace de Besov limite B∞,11. On établit également un critère de prolongement dans lʼesprit de celui de Beale, Kato et Majda (1984) [2] pour le cas homogène. Dans la dernière partie de lʼarticle, on donne des minorations pour le temps de vie des solutions du système. En dimension deux, on montre que ce temps de vie tend vers lʼinfini lorsque la densité tend à être homogène. À notre connaissance, il sʼagit du premier résultat de ce type pour le système dʼEuler incompressible à densité variable.

VL - 96 UR - http://www.sciencedirect.com/science/article/pii/S0021782411000511 ER - TY - JOUR T1 - Well-posed infinite horizon variational problems on a compact manifold JF - Proceedings of the Steklov Institute of Mathematics. Volume 268, Issue 1, 2010, Pages 17-31 Y1 - 2010 A1 - Andrei A. Agrachev AB - We give an effective sufficient condition for a variational problem with infinite horizon on a compact Riemannian manifold M to admit a smooth optimal synthesis, i. e., a smooth dynamical system on M whose positive semi-trajectories are solutions to the problem. To realize the synthesis, we construct an invariant Lagrangian submanifold (well-projected to M) of the flow of extremals in the cotangent bundle T*M. The construction uses the curvature of the flow in the cotangent bundle and some ideas of hyperbolic dynamics PB - SISSA UR - http://hdl.handle.net/1963/6458 U1 - 6404 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - CHAP T1 - WDVV equations and Frobenius manifolds T2 - Encyclopedia of Mathematical Physics. Vol 1 A : A-C. Oxford: Elsevier, 2006, p. 438-447 Y1 - 2006 A1 - Boris Dubrovin JF - Encyclopedia of Mathematical Physics. Vol 1 A : A-C. Oxford: Elsevier, 2006, p. 438-447 PB - SISSA SN - 0125126611 UR - http://hdl.handle.net/1963/6473 U1 - 6419 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - Wetting of rough surfaces: a homogenization approach JF - Proc. R. Soc. Lon. Ser. A 461 (2005) 79-97 Y1 - 2005 A1 - Antonio DeSimone A1 - Giovanni Alberti AB - The contact angle of a drop in equilibrium on a solid is strongly affected by the roughness of the surface on which it rests. We study the roughness-induced enhancement of the hydrophobic or hydrophilic properties of a solid surface through homogenization theory. By relying on a variational formulation of the problem, we show that the macroscopic contact angle is associated with the solution of two cell problems, giving the minimal energy per unit macroscopic area for a transition layer between the rough solid surface and a liquid or vapor phase. Our results are valid for both chemically heterogeneous and homogeneous surfaces. In the latter case, a very transparent structure emerges from the variational\\napproach: the classical laws of Wenzel and Cassie-Baxter give bounds for the optimal energy, and configurations of minimal energy are those leading to the smallest macroscopic contact angle in the hydrophobic case, to the largest one in the hydrophilic case. UR - http://hdl.handle.net/1963/2253 U1 - 1994 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Well-posedness for general 2x2 systems of conservation laws JF - Mem. Amer. Math. Soc. 169 (2004), no. 801, x+170 pp. Y1 - 2004 A1 - Fabio Ancona A1 - Andrea Marson PB - SISSA Library UR - http://hdl.handle.net/1963/1241 U1 - 2702 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Warped products with special Riemannian curvature JF - Bol. Soc. Brasil. Mat. (N.S.) Y1 - 2001 A1 - Marco Bertola A1 - Gouthier, Daniele VL - 32 ER - TY - BOOK T1 - Well-posedness of the Cauchy problem for n x n systems of conservation laws T2 - Mem. Amer. Math. Soc. 146 (2000), no. 694, 134 p. Y1 - 2000 A1 - Alberto Bressan A1 - Graziano Crasta A1 - Benedetto Piccoli JF - Mem. Amer. Math. Soc. 146 (2000), no. 694, 134 p. PB - American Mathematical Society UR - http://hdl.handle.net/1963/3495 N1 - Chapter 1 and 2 U1 - 769 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Workshop on point interactions, Trieste, 21-23 December 1992 Y1 - 1993 A1 - Gianfausto Dell'Antonio PB - SISSA Library UR - http://hdl.handle.net/1963/71 U1 - 52 U2 - LISNU U3 - Interdisciplinary Laboratory for Advanced Studies ER - TY - JOUR T1 - Weak convergence of measures on spaces of semicontinuous functions. JF - Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 79 (1985), no. 5, 98-106 Y1 - 1985 A1 - Gianni Dal Maso A1 - Ennio De Giorgi A1 - Luciano Modica PB - SISSA Library UR - http://hdl.handle.net/1963/463 U1 - 3440 U2 - Mathematics U3 - Mathematical Physics ER -