MOX Reports
The preprint collection of the Laboratory for Modeling and Scientific Computation MOX. It mainly contains works on numerical
analysis and mathematical modeling applied to engineering problems. MOX web site is mox.polimi.it
Found 1238 products
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28/2015 - 06/13/2015
Taffetani, M.; Ciarletta, P.
Beading instability in soft cylindrical gels with capillary energy: weakly non-linear analysis and numerical simulations | Abstract | | Soft cylindrical gels can develop a long-wavelength peristaltic pattern driven by a competition between surface tension and bulk elastic energy. In contrast to the Rayleigh-Plateau instability for viscous fluids, the macroscopic shape in soft solids evolves toward a stable beading, which strongly differs from the buckling arising in compressed elastic cylinders.
This work proposes a novel theoretical and numerical approach for studying the onset and the non-linear development of the elastocapillary beading in soft cylinders, made of neo-Hookean hyperelastic material with capillary energy at the free surface, subjected to axial stretch. Both a theoretical study, deriving the linear and the weakly non-linear stability analyses for the problem, and numerical simulations, investigating the fully non-linear evolution of the beaded morphology, are performed. The theoretical results prove that an axial elongation can not only favour the onset of beading, but also determine the nature of the elastic bifurcation. The fully non-linear phase diagrams of the beading are also derived from finite element numerical simulations, showing two peculiar morphological transitions when varying either the axial stretch or the material properties of the gel. Since the bifurcation is found to be subcritical for very slender cylinders, an imperfection sensitivity analysis is finally performed. In this case, it is shown that a surface sinusoidal imperfection can resonate with the corresponding marginally stable solution, thus selecting the emerging beading wavelength.
In conclusion, the results of this study provide novel guidelines for controlling the beaded morphology in different experimental conditions, with important applications in micro-fabrication techniques, such as electrospun fibres. |
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27/2015 - 05/25/2015
Marron, J.S.; Ramsay, J.O.; Sangalli, L.M.; Srivastava, A.
Functional Data Analysis of Amplitude and Phase Variation | Abstract | | The abundance of functional observations in scientific endeavors has led to a significant development in tools for functional data analysis (FDA). This kind of data comes with several challenges: infinite dimensionality
of function spaces, observation noise, and so on. However, there is another interesting phenomena that creates problems in FDA. The functional data often comes with lateral displacements/deformations in curves, a phenomenon which is different from the height or amplitude variability and is termed phase variation. The presence of phase variability artificially often inflates data variance, blurs underlying data structures and distorts principal components. While the separation and/or removal of phase from amplitude data is desirable, this is a difficult problem. In particular, a commonly-used alignment procedure, based on minimizing the L2 norm between functions, does not provide satisfactory results. In this paper we motivate the importance of dealing with the phase variability and summarize several current ideas for separating phase and amplitude components. These approaches differ in: (1) the definition and mathematical representation of phase variability, (2) the objective functions that are used in functional data alignment, and (3) the algorithmic tools for solving estimation/optimization problems. We use simple examples to illustrate various approaches and to provide useful contrast between them. |
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26/2015 - 05/25/2015
Tagliabue, A.; Dede', L.; Quarteroni, A.
Nitsche’s Method for Parabolic Partial Differential Equations with Mixed Time Varying Boundary Conditions | Abstract | | We investigate a finite element approximation of an initial boundary value problem associated with parabolic Partial Differential Equations endowed with mixed time varying boundary conditions, switching from essential to natural and viceversa. The switching occurs both in time and in different portions of the boundary. For this problem, we apply and extend the Nitsche’s method presented in [Juntunen and Stenberg,Mathematics of Computation, 2009] to the case of mixed time varying boundary conditions. After proving existence and numerical stability of the full discrete numerical solution obtained by using the ?-method for time discretization, we present and discuss a numerical test that compares our method to a standard approach based on remeshing and projection procedures. |
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25/2015 - 05/25/2015
Del Pra, M.; Fumagalli, A.; Scotti, A.
Well posedness of fully coupled fracture/bulk Darcy flow with XFEM | Abstract | | In this work we consider the coupled problem of Darcy’s flow in a fracture and the surrounding porous medium. The fracture is represented as a (d ? 1)-dimensional interface and it is non-matching with the computational grid thanks to a suitable XFEM enrichment of the mixed finite element spaces. In the existing literature well posedness has been proven for the discrete problem in the hypothesis of given solution in the fracture. This works provides theoretical results on the stability and convergence of the discrete, fully coupled problem, yielding sharp conditions on the fracture geometry and on the computational grid to ensure that the inf-sup conditions is satisfied by the enriched spaces, as confirmed by numerical experiments.
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24/2015 - 05/15/2015
Bonaventura, L:
Local Exponential Methods: a domain decomposition approach to exponential time integration of PDE. | Abstract | | A local approach to the time integration of PDEs by exponential methods is
proposed, motivated by theoretical estimates by A.Iserles on the decay of off-diagonal terms in the exponentials of sparse matrices. An overlapping domain decomposition technique is outlined, that allows to replace the computation of a global exponential matrix by a number of independent and easily parallelizable local problems. Advantages and potential
problems of the proposed technique are discussed. Numerical experiments on simple, yet relevant model problems show that the resulting method allows to increase computational efficiency with respect to standard implementations of exponential methods. |
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23/2015 - 05/08/2015
Paolucci, R.; Mazzieri, I.; Smerzini, C.
Anatomy of strong ground motion: near-source records and 3D physics-based numerical simulations of the Mw 6.0 May 29 2012 Po Plain earthquake, Italy | Abstract | | Stimulated by the recent advances in computational tools for the simulation of seismic wave propagation problems in realistic geologic environments, this paper presents a 3D physics-based numerical study on the prediction of earthquake ground motion in the Po Plain, with reference to the Mw 6.0 May 29 2012 earthquake.
To respond to the validation objectives aimed at reproducing with a reasonable accuracy some of the most peculiar features of the near-source strong motion records and of the damage distribution, this study required a sequence of investigations, starting from the analysis of a nearly unprecedented set of near-source records, to the calibration of an improved kinematic seismic source model, up to the development of a 3D numerical model of the portion of the Po Plain interested by the earthquake, including the irregular buried morphology, with sediment thickness varying from few tens of m to some km. The spatial resolution of the numerical model is suitable to propagate up to about 1.5 Hz. Numerical simulations were performed using the open-source high-performance code SPEED, based on the Discontinuous Galerkin Spectral Elements (DGSE) method.
The 3D numerical model coupled with the updated slip distribution along the rupturing fault proved successful to reproduce with reasonable accuracy, measured through quantitative goodness-of-fit criteria, the most relevant features of the observed ground motion both at the near- and far-field scales. These include: (i) the large fault normal velocity peaks at the near-source stations driven by up-dip directivity effects; (ii) the small-scale variability at short distance from the source, resulting in the out-of-phase motion at stations separated by only 3 km distance; (iii) the propagation of prominent trains of surface waves, especially in the Northern direction, induced by the irregular buried morphology in the near-source area; (iv) the map of earthquake-induced ground uplift with maximum values of about 10 cm, in substantial agreement with satellite measurements; and (v) the two-lobed pattern of the peak ground velocity map, well correlated with the distribution of macroseismic intensity. |
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22/2015 - 05/05/2015
Bonaventura, L.; Ferretti, R.
Flux form Semi-Lagrangian methods for parabolic problems | Abstract | | A semi-Lagrangian method for parabolic problems is proposed,
that extends previous work by the authors to achieve a fully conservative, flux-form discretization of linear and nonlinear diffusion equations.
A basic consistency and convergence analysis are proposed. Numerical examples
validate the proposed method and display its potential for consistent semi-Lagrangian discretization of advection--diffusion and nonlinear parabolic problems. |
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21/2015 - 04/28/2015
Arena, M.; Azzone, G.; Secchi, P.; Vantini, S.
Reputational risk and corporate finance: A multi-event model | Abstract | | This paper develops a model for the evaluation of reputational risk and explores if certain characteristics of negative events happening to a company can explain their reputational impacts. To this aim, the paper adopts the share market value as a synthetic measure of a company’s ability to create economic value and explores the reaction of the share market to the announcement of negative events (e.g. protests, accidents, corporate misconducts).
The proposed model contributes to prior research in this field with three innovative dimensions. It applies to events that have a limited impact from an operational perspective (e.g. protests, small environmental events) but could have a considerable reputational effect. It applies to different types of events that can potentially affect the stakeholders’ expectations and perceptions. It addresses the determinants of reputational risk, exploring which characteristics of an event explain the share market reaction.
The empirical analysis is based on data collected over a timeframe of ten years, concerning a leading multinational company, that competes in the Oil & Gas industry and is listed on NY Stock Exchange. 67 events involving this company in this period of time are analysed through the proposed model, leading to the identification of a sub-set of events which significant reputational events are associated with and to the exploration of different factors that can explain the relevance of the reported reputational impacts. |
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