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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07/2015 - 02/05/2015
Giovanardi, B.; Scotti, A.; Formaggia, L.; Ruffo, P.
A general framework for the simulation of geochemical compaction | Abstract | | We propose a mathematical model and a numerical scheme to describe compaction
processes in a sedimentary rock layer undergoing both mechanical and
geochemical processes. We simulate the sedimentation process by providing a
sedimentation rate and we account for chemical reactions using simplified kinetics
describing either the conversion of a solid matrix into a fluid, as in the case of
kerogen degradation into oil, or the precipitation of a mineral solute on the solid
matrix of the rock. We use a Lagrangian description that enables to recast the
equations in a fixed frame of reference. We present an iterative splitting scheme
that allows solving the set of governing equations efficiently in a sequential manner.
We assess the performances of this strategy in terms of convergence and mass
conservation. Some numerical experiments show the capability of the scheme to
treat two test cases, one concerning the precipitation of a mineral, the other the
dissolution of kerogen. |
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08/2015 - 02/02/2015
Agosti, A.; Formaggia, L.; Giovanardi, B.; Scotti, A.
Numerical simulation of geochemical compaction with discontinuous reactions | Abstract | | The present work deals with the numerical simulation of porous media subject to the coupled effects of mechanical compaction and reactive flows that can significantly alter the porosity due to dissolution, precipitation or transformation of the solid matrix. These chemical processes can be effectively modelled by ODEs with discontinuous right hand side, where the discontinuity depends on time and on the solution itself. Filippov theory can be applied to prove existence and to determine the solution behaviour at the discontinuities. From the numerical point of view, tailored numerical schemes are needed to guarantee positivity, mass conservation and accuracy. In particular, we rely on an event-driven approach such that, if the trajectory crosses a discontinuity, the transition point is localized exactly and integration is restarted accordingly.
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05/2015 - 01/29/2015
Chen, P.; Quarteroni, A.; Rozza, G.
Reduced order methods for uncertainty quantification problems | Abstract | | This work provides a review on reduced order methods in solving uncertainty quantification problems. A quick introduction of the reduced order methods, including proper orthogonal decomposition and greedy reduced basis methods, are presented along with the essential components of general greedy algorithm, a posteriori error estimation and Offline-Online decomposition. More advanced reduced order methods are then developed for solving typical uncertainty quantification problems involving pointwise evaluation and/or statistical integration, such as failure probability evaluation, Bayesian inverse problems and variational data assimilation. Three expository examples are provided to demonstrate the efficiency and accuracy of the reduced order methods, shedding the light on their potential for solving problems dealing with more general outputs, as well as time dependent, vectorial noncoercive parametrized |
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01/2015 - 01/26/2015
Pini, A.; Stamm, A.; Vantini, S.
Hotelling s $T^2$ in functional Hilbert spaces | Abstract | | The field of statistics is at the cusp of a revolution in the way data is collected by measuring instruments. Massive information is retrieved in real-time and/or spatially-referenced, hence producing new kind of data: functional data. Statistical inference for functional data is particularly challenging as it is an extreme case of high-dimensional data for which, no matter how large the sample is, information will always be insufficient to fully characterize the underlying model.
In detail, after a historical excursus over the test statistics introduced for approaching the problem of testing the mean, we provide a generalization of Hotelling s $T^2$ on any functional Hilbert space, naturally dubbed functional Hotelling s $T^2$. We discuss a nonparametric permutational framework that enables statistical testing for the mean function of a population as well as for the difference between the mean functions of two populations. Within this framework, we show how a number of state-of-the-art test statistics can be seen as approximations of functional $T^2$ statistic hereby proposed. |
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02/2015 - 01/26/2015
Menafoglio, A.; Petris, G.
Kriging for Hilbert-space valued random fields: the Operatorial point of view | Abstract | | We develop a comprehensive framework for linear spatial prediction in Hilbert spaces. We explore the problem of Best Linear Unbiased (BLU) prediction in Hilbert spaces through an original point of view, based on a new Operatorial definition of Kriging. We ground our developments on the theory of Gaussian processes in function spaces and on the associated notion of measurable linear transformation. We prove that our new setting allows (a) to derive an explicit solution to the problem of Operatorial Ordinary Kriging, and (b) to establish the relation of our novel predictor with the key concept of conditional expectation of a Gaussian measure. Our new theory is posed as a unifying theory for Kriging, which is shown to include the Kriging predictors proposed in the literature on Functional Data through the notion of finite-dimensional approximations. Our original viewpoint to Kriging offers new relevant insights for the geostatistical analysis of either finite- or infinite-dimensional georeferenced dataset. |
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03/2015 - 01/26/2015
Abramowicz, K.; de Luna, S.; Häger, C.; Pini, A.; Schelin, L.; Vantini, S.
Distribution-Free Interval-Wise Inference for Functional-on-Scalar Linear Models | Abstract | | We introduce a distribution-free procedure for testing a functional-on-scalar linear model with fixed effects.
The procedure does not only test the global hypothesis on all the domain, but also selects the intervals where statistically significant effects are detected.
We prove that the proposed tests are provided with an asymptotic interval-wise control of the family-wise error rate, i.e., the probability of falsely rejecting any interval of true null hypotheses.
The procedure is then applied to one-leg hop data from a study on anterior cruciate ligament injury. We compare knee kinematics of three groups of individuals, taking individual-specific covariates into account. |
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04/2015 - 01/26/2015
Arioli, G.; Gazzola, F.
On a nonlinear nonlocal hyperbolic system modeling suspension bridges | Abstract | | We suggest a new model for the dynamics of a suspension bridge through a system of nonlinear nonlocal hyperbolic differential equations.
The equations are of
second and fourth order in space and describe the behavior of the main components of the bridge: the deck, the sustaining cables and the connecting
hangers. We perform a careful energy balance and we derive the equations from a variational principle. We then prove existence and uniqueness for
the resulting problem. |
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62/2014 - 12/17/2014
Andrà, C.; Parolini, N.; Verani, M.
Using gambling simulators to foster awareness about gambling risks | Abstract | | Stemming from an interest in developing suitable didactical activities to prevent gambling abuse during the school years, this paper explores the use of an Android app that simulates the outcomes of a famous Italian instant lottery. Some features that characterise the phenomenon of gambling abuse are sketchily recalled, the Android app is presented and an example from classroom activities is discussed. We conclude that the simulator support probabilistic thinking and understanding of models about gambling, as traditional random generators do, and also exploits emotional reactions, such as shock, which allow curiosity to emerge and pave the road towards deeper understanding. |
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