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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11/2017 - 02/20/2017
Ferro, N.; Micheletti, S.; Perotto, S.
Anisotropic Mesh Adaptation for Crack Propagation Induced by a Thermal Shock | Abstract | | In this paper we focus on the thermo-mechanical model which
describes crack genesis and propagation in brittle materials induced by a thermal shock.
Our goal is to provide an efficient numerical technique which employs a computational finite element mesh finely customized to the problem at hand to simulate such phenomena.
In particular, we generate automatically adapted anisotropic grids able to closely follow the narrow bands
of the damage, driven by a theoretically sound mathematical tool.
We carry out two numerical tests to assess the computational performance of the proposed method. |
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10/2017 - 02/20/2017
Pini, A.; Stamm, A.; Vantini, S.
Hotelling's $T^2$ in separable Hilbert spaces | Abstract | | We address the problem of finite-sample null hypothesis significance testing on the mean element of a random variable that takes value in a generic separable Hilbert space. For this purpose, we propose a (re)definition of Hotelling's $T^2$ statistic that naturally expands to any separable Hilbert space that we further embed within a permutation inferential approach. In detail, we present a unified framework for making inference on the mean element of Hilbert populations based on Hotelling's $T^2$ statistic, using a permutation-based testing procedure of which we prove finite-sample exactness and consistency; we showcase the explicit form of Hotelling's $T^2$ statistic in the case of some famous spaces used in functional data analysis (i.e., Sobolev and Bayes spaces); we propose simulations and a case study that demonstrate the importance of the space into which one decides to embed the data; we provide an implementation of the proposed tools in the R package fdahotelling |
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09/2017 - 02/20/2017
Antonietti, P.F.; Ferroni, A.; Mazzieri, I.; Paolucci, R.; Quarteroni, A.; Smerzini, C.; Stupazzini, M.
Numerical modeling of seismic waves by Discontinuous Spectral Element methods | Abstract | | We present a comprehensive review of Discontinuous Galerkin Spectral Element (DGSE) methods on hybrid hexahedral/tetrahedral grids for the numerical modeling of the ground motion induced by large earthquakes. DGSE methods combine the flexibility of discontinuous Galerkin methods to patch together, through a domain decomposition paradigm, Spectral Element blocks where high-order polynomials are used for the space discretization coupled with a leap-frog time marching schemes. This approach allows local adaptivity on discretization parameters, thus improving the quality of the solution without affecting the computational costs. The theoretical properties of the semidis- crete formulation are also revised, including well-posedness, stability and error estimates. A discussion on the dissipation, dispersion and stability properties of the fully-discrete (in space and time) formulation is also presented. The capabilities of the present approach are demonstrated through a set on computations of realistic earthquake scenarios obtained using the code SPEED (http://speed.mox.polimi.it), an open-source code specifically designed for the numerical modeling of large-scale seismic events jointly developed at Politecnico di Milano by The Laboratory for Modeling and Scientific Computing MOX and by the Department of Civil and Environmental Engineering. |
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08/2017 - 01/31/2017
Ambrosi, D.; Beloussov, L.V.; Ciarletta, P.
Mechanobiology and morphogenesis in living matter: a survey | Abstract | | Morphogenesis in living tissues is the paramount example of a time- and space-dependent orchestration of living matter where shape and order emerge
from undifferentiated initial conditions. The genes encode the protein expression that eventually drives the emergence of the phenotype, while energy supply and cell-to-cell communication mechanisms are necessary to such a process. The overall control of the system likely exploits the laws of chemistry and physics through robust and universal processes. Even if the identification of the communication mechanisms is a question of fundamental nature, a long-standing investigation settled in the realm of chemical factors only (also known as morphogens) faces a number of apparently unsolvable questions. In this paper, we investigate at what extent mechanical forces, alone or through their biological feedbacks, can direct some basic aspects of morphogenesis in development biology. In this branch of mechano-biology, we discuss the typical rheological regimes of
soft living matter and the related forces, providing a survey on how local mechanical feedbacks can control global size or even gene expression. We finally highlight the pivotal role of nonlinear mechanics to explain the
emergence of complex shapes in living matter.
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07/2017 - 01/27/2017
Cabassi A.; Pigoli D.; Secchi P.; Carter P.A.
Permutation tests for the equality of covariance operators of functional data with applications to evolutionary biology | Abstract | | In this paper, we generalize the metric-based permutation test for the equality of covariance operators proposed by Pigoli et al. (2014) to the case of multiple samples of functional data. To this end, the non-parametric combination methodology of Pesarin and Salmaso (2010) is used to combine all the pairwise comparisons between samples into a global test. Different combining functions and permutation strategies are reviewed and analyzed in detail. The resulting test allows to make inference on the equality of the covariance operators of multiple groups and, if there is evidence to reject the null hypothesis, to identify the pairs of groups having different covariances. It is shown that, for some combining functions, step-down adjusting procedures are available to control for the multiple testing problem in this setting. The empirical power of this new test is then explored via simulations and compared with those of existing alternative approaches in different scenarios. Finally, the pro- posed methodology is applied to data from wheel running activity experiments, that used selective breeding to study the evolution of locomotor behavior in mice. |
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06/2017 - 01/27/2017
Ekin, T.; Ieva, F.; Ruggeri, F.; Soyer, R.
On the Use of the Concentration Function in Medical Fraud Assessment | Abstract | | We propose a simple, but effective, tool to detect possible anomalies in the services prescribed by a health care provider (HP) compared to his/her colleagues in the same field and environment. Our method is based on the concentration function which is an extension of the Lorenz curve widely used in describing uneven distribution of wealth in a population. The proposed tool provides a graphical illustration of a possible anomalous behavior of the HPs and it can be used as a pre-screening device for further investigations of potential medical fraud. |
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05/2017 - 01/20/2017
Menafoglio, A.; Hron, K.; Filzmoser, P.
Logratio approach to distributional modeling | Abstract | | Symbolic data analysis (SDA) provides a unified approach to analyze distributional data, resulting from capturing intrinsic variability of groups of individuals as input observations. In parallel to the SDA approach, a concise methodology has been developed since the early 1980s to deal with compositional data — i.e., data carrying only relative information — through the logratios of their parts. Most methods in compositional data analysis aims to treat multivariate observations which can be identified with probability functions of discrete distributions. Nevertheless, a methodology to capture the specific features of continuous distributions (densities) has been recently introduced. The aim of this work is to describe a general setting that includes both the discrete and the continuous setting, and to provide specific details to both frameworks focusing on the implications on SDA. The theoretical developments are illustrated with real-world case studies. |
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04/2017 - 01/19/2017
Dede', L; Garcke, H.; Lam K.F.
A Hele-Shaw-Cahn-Hilliard model for incompressible two-phase flows with different densities | Abstract | | Topology changes in multi-phase fluid flows are difficult to model within a traditional sharp interface theory. Diffuse interface models turn out to be an attractive alternative to model two-phase flows. Based on a Cahn-Hilliard-Navier-Stokes model introduced by Abels, Garcke and Grun (Math. Models Methods Appl. Sci. 2012), which uses a volume averaged velocity, we derive a diffuse interface model in a Hele-Shaw geometry, which in the case of non-matched densities, simplifies an earlier model of Lee, Lowengrub and Goodman (Phys. Fluids 2002). We recover the classical Hele-Shaw model as a sharp interface limit of the diffuse interface model. Furthermore, we show the existence of weak solutions and present several numerical computations including situations with rising bubbles and fingering instabilities. |
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