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 1249 products
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15/2011 - 03/30/2011
Argiento, R.; Guglielmi, A.; Soriano J.
A semiparametric Bayesian generalized linear mixed model for the reliability of Kevlar fibres | Abstract | | We analyze the reliability of NASA composite pressure vessels using a new Bayesian semiparametric model. The dataset consists of lifetimes of pressure vessels, wrapped with a Kevlar fiber, grouped by spool, subject to different stress levels; 10% of data are right censored. The model we consider is a regression on the log-scale for the lifetimes, with fixed (stress) and random (spool) effects. The prior of the spool parameters is nonparametric, namely they are a sample from a normalized generalized gamma process, which encompasses the well-known Dirichlet process. The nonparametric prior is assumed to robustify inferences to mispecification of the parametric prior. Here, this choice of likelihood and prior yields a new Bayesian model in reliability analysis. Via a Bayesian hierarchical approach, it is easy to analyze the reliability of the Kevlar fiber by predicting quantiles of the failure time when a new spool is selected at random from the population of spools. Moreover, for comparative purposes we review the most interesting frequentist and Bayesian models analyzing this dataset. Our credibility intervals of the quantiles of interest for a new random spool are narrower than those derived by previous Bayesian parametric literature. Additionally, the discreteness of the random-effects distribution induces a natural clustering of the spools into three different groups, which is in accordance with the frequentist spool rankings.
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14/2011 - 03/29/2011
Antonietti, P.F.; Mazzieri, I.; Quarteroni, A.; Rapetti, F.
Non-Conforming High Order Approximations for the Elastic Wave Equation | Abstract | | In this paper we formulate and analyze two non conforming high order strategies for approximating the solution of elastic wave problems in heterogeneous media, namely the Mortar Spectral Element Method and the Discontinuous Galerkin Spectral Element Method.
Starting from a common variational formulation we make a full comparison of the two techniques from the points of view of accuracy, convergence, grid dispersion and stability. |
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13/2011 - 03/15/2011
Lombardi, M.; Parolini, N.; Quarteroni, A.; Rozza, G.
Numerical simulation of sailing boats: dynamics, FSI, and shape optimization | Abstract | | The numerical simulation of free-surface flows around sailing boats is a complex topic that addresses multiple mathematical tasks: the correct study of the flow field around a rigid hull, the numerical simulation of the hull dynamics, the deformation of the sails and appendages under transient external conditions like gusts of wind or wave patterns and, overall, the coupling among all these components. In this paper, we present some recent advances that have been achieved in different research topics related to yacht design and performance prediction. In particular, we describe the numerical algorithms that have been developed in the framework of open-source libraries for the simulation of free-surface hydrodynamics and boat dynamics, as well as for the analysis of the fluid-structure interaction between wind and sails. Moreover, an algorithm for shape optimization, based on the solution of the adjoint problem and combined with the Free Form Deformation (FFD) method for the shape parametrization and mesh motion, is presented and discussed. Theoretical and methodological aspects are described and the first preliminary results are reported. |
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12/2011 - 03/14/2011
Miglio E.; Cuffaro M.
Tectonic evolution at mid-ocean ridges: geodynamics and numerical modeling | Abstract | | Tectonic evolution at rift zones is commonly considered symmetric along mid-ocean ridges, when modeling with relative plate motions and steady-state processes. However, tectonic features are generally asymmetric, as provided by geological a geophysical data. A better way to understand dynamics of the lithosphere at rift zones, and lithosphere/mantle interactions corresponds to
absolute plate kinematic analyses, i.e., with respect to the mantle, modeling time-dependent tectonic processes. We performed numerical simulations of plate-driven mantle flow beneath mid-ocean ridges and we considered a time-dipendent flow induced by the motion of overlying rigid plates in an
incompressible viscous mantle, using plate velocities obtained in the hotspot reference frame, as boundary conditions.
This implies that plates along a ridge, and the ridge itself, move toward the same direction, but with different velocities, relative to the mantle, and the separation between plates triggers mantle upwelling. Numerical solutions for viscosity flow beneath plates that thicken with increasing age are presented. The mantle can be modeled as a viscous fluid, and its dynamics can be described using the Stokes equations and thermal effects, and a finite element approach has been adopted to obtain numerical solutions. Results show an asymmetric thickening of oceanic plates along the ridge, as suggested by the observations, and provide useful relationships between mantle temperature and thickness of the oceanic lithosphere. |
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11/2011 - 02/20/2011
Formaggia, L.; Minisini, S.; Zunino, P.
Stent a rilascio di farmaco: una storia di successo per la matematica applicata | Abstract | | In the last decades the adoption of mathematical models to support medical research has found a considerable increase of interest, stimulating
the activity of applied mathematicians. A better understanding of the physical and biological phenomena together with the availability of powerful and affordable computers has prompted the use of numerical simulation as a complement, even if not yet as a substitute, of animal experimentation and clinical trials. In the case considered here, namely that of particular drug
eluting devices used in the treatment of arteriosclerosis, it allows for the evaluation of the effect of different designs of the device, or different type of drugs. In this article we give a review of mathematical models used for simulating the functioning of drug eluting stents. We start by considering the simplest models, based on empirical formulae or ordinary differential equations, up to models based on systems of partial differential equations that describe the drug elution processes coupled with the diffusion and transport of the drug in biological tissues and blood flow. |
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10/2011 - 02/19/2011
Zunino, P.; Vesentini, S.; Porpora, A.; Soares, J.S.; Gautieri, A.; Redaelli, A.
Multiscale computational analysis of degradable polymers | Abstract | | Degradable materials have found a wide variety of applications in the biomedical field ranging from sutures, pins and screws for orthopedic surgery, local drug delivery, tissue engineering scaffolds, and endovascular stents. Polymer degradation is the irreversible chain scission process that breaks polymer chains down to oligomers and, finally, to monomers. These changes, which take place at the molecular scale, propagate through the space/time scales and not only affect the
capacity of the polymer to release drugs, bu also hamper the overall mechanical behavior of the device, whose spatial scale is denoted as macro-scale. A bottom-up multiscale analysis is applied to model the degradation mechanism which takes
place in PLA matrices. The macroscale model is based on diffusion-reaction equations for hydrolytic polymer degradation and erosion while the microscale model is based on atomistic simulations to predict the water diffusion as a function of the swelling degree of the PLA matrix. The diffusion coefficients are then passed to the macroscale model. In conclusion, the proposed multiscale analysis is capable to predict the evolution with time of several properties of water/PLA mixtures, according to the change of relevant indicators such as the extent of degradation
and erosion of the PLA matrix.
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09/2011 - 02/18/2011
Pigoli, D.; Sangalli, L.
Wavelets in Functional Data Analysis: estimation of multidimensional curves and their derivatives | Abstract | | A wavelet-based method is proposed to obtain accurate estimates of curves in more than one dimension and of their derivatives. By means
of simulation studies, we compare this novel method to another locally-adaptive estimation technique for multidimensional functional data, based on free-knot regression splines. This comparison shows that the proposed method is particularly attractive when the curves to be estimated present strongly localized features. The multidimensional wavelet estimation method is thus applied to multi-lead electrocardiogram records, where strongly localized features are indeed expected. |
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08/2011 - 02/17/2011
Ieva, F.; Paganoni, A.M.; Secchi, P.
Mining Administrative Health Databases for epidemiological purposes: a case study on Acute Myocardial Infarctions diagnoses | Abstract | | We present a pilot data mining analysis on the subset of the Public Health Database of Lombardia Region concerning hospital discharge data relative to Acute Myocardial Infarctions without ST segment elevation (NON-STEMI). The analysis is carried out using non linear semi parametric and parametric mixed effects models, in order to detect different patterns of growth in the number of NON-STEMI
diagnoses within the 30 largest clinical structures of Lombardia Region, along the time period 2000-2007. The analysis is a seminal example of statistical support to decision makers in clinical context, aimed at monitoring the diffusion of new procedures and the effects of health policy interventions. |
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