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
-
21/2016 - 05/12/2016
Ambrosi, D.; Zanzottera, A.
Mechanics and polarity in cell motility | Abstract | | The motility of a fish keratocyte on a flat substrate exhibits two distinct regimes: the non- migrating and the migrating one. In both configurations the shape is fixed in time and, when the cell is moving, the velocity is constant in magnitude and direction. Transition from a stable configuration to the other one can be produced by a mechanical or chemotactic perturbation. In order to point out the mechanical nature of such a bistable behaviour, we focus on the actin dynamics inside the cell using a minimal mathematical model. While the protein diffusion, recruitment and segregation govern the polarization process, we show that the free actin mass balance, driven by diffusion, and the polymerized actin retrograde flow, regulated by the active stress, are sufficient ingredients to account for the motile bistability. The length and velocity of the cell are predicted on the basis of the parameters of the substrate and of the cell itself. The key physical ingredient of the theory is the exchange among actin phases at the edges of the cell, that plays a central role both in kinematics and in dynamics. |
-
20/2016 - 05/05/2016
Wilhelm, M.; Sangalli, L.M.
Generalized Spatial Regression with Differential Regularization | Abstract | | We aim at analyzing geostatistical and areal data observed over irregularly shaped spatial domains and having a distribution within the exponential family. We propose a generalized additive model that allows to account for spatially-varying covariate information. The model is fitted by maximizing a penalized log-likelihood function, with a roughness penalty term that involves a differential quantity of the spatial field, computed over the domain of interest. Efficient estimation of the spatial field is achieved resorting to the finite element method, which provides a basis for piecewise polynomial surfaces. The proposed model is illustrated by an application to the study of criminality in the city of Portland, Oregon, USA. |
-
19/2016 - 05/05/2016
Guerciotti, B.; Vergara, C.
Computational comparison between Newtonian and non-Newtonian blood rheologies in stenotic vessels | Abstract | | This work aims at investigating the influence of non-Newtonian blood rheology on the hemodynamics of 3D patient-specific stenotic vessels, by means of a comparison of some numerical results with the Newtonian case. In particular, we consider two carotid arteries with severe stenosis and a stenotic coronary artery treated with a bypass graft, in which we virtually vary the degree of stenosis. We perform unsteady numerical simulations based on the Finite Element method using the Carreau-Yasuda model to describe the non-Newtonian blood rheology. Our results show that velocity, vorticity and wall shear stress distributions are moderately influenced by the non-Newtonian model in case of stenotic carotid arteries. On the other hand, we observed that a non-Newtonian model seems to be important in case of stenotic coronary arteries, in particular to compute the relative residence time which is greatly affected by the rheological model. |
-
18/2016 - 04/11/2016
Ferroni, A.; Antonietti, P.F.; Mazzieri, I.; Quarteroni, A.
Dispersion-dissipation analysis of 3D continuous and discontinuous spectral element methods for the elastodynamics equation | Abstract | | In this paper we present a three dimensional dispersion and dissipation analysis for both the semi-discrete and the fully discrete approximation of the elastodynamics equation based on the plane wave method. For space discretization we compare different approximation strategies, namely the continuous and discontinuous spectral element method on both tetrahedral and hexahedral elements. The fully discrete scheme is then obtained exploiting a leap-frog time integration scheme. Several numerical results are presented and discussed. |
-
17/2016 - 04/08/2016
Penati, M.; Miglio, E.
A new mixed method for the Stokes equations based on stress-velocity-vorticity formulation | Abstract | | In this paper, we develop and analyze a mixed finite element method for the Stokes flow. This method is based on a stress-velocity-vorticity formulation. A new discretization is proposed: the stress is approximated using the Raviart-Thomas elements, the velocity and the vorticity by piecewise discontinuous polynomials. It is shown that if the orders of these spaces are properly chosen then the advocated method is stable. We derive error estimates for the Stokes problem, showing optimal accuracy for both the velocity and vorticity. |
-
16/2016 - 04/06/2016
Agosti, A.; Antonietti, P.F.; Ciarletta, P.; Grasselli, M.; Verani, M.
A Cahn-Hilliard type equation with degenerate mobility and single-well potential. Part I: convergence analysis of a continuous Galerkin finite element discretization. | Abstract | | We consider a Cahn-Hilliard type equation with degenerate mobility
and single-well potential of Lennard-Jones type. This equation models the
evolution and growth of biological cells such as solid tumors. The degeneracy set of the mobility and the singularity set of the cellular potential do not coincide, and the absence of cells is an unstable equilibrium configuration of the potential. This feature introduces a nontrivial difference with respect to the Cahn-Hilliard equation analyzed in the literature. We formulate a continuous finite element approximation of the problem, where the positivity of the solution is enforced through a discrete variational inequality. We prove the existence and uniqueness of the discrete solution together with the convergence to the weak solution. We present simulation results in one and two space dimensions. We also study the dynamics of the spinodal decomposition and the growth and scaling laws of phase ordering dynamics.
In this case we find similar results to the ones obtained in standard phase
ordering dynamics and we highlight the fact that the asymptotic behavior
of the solution is dominated by the mechanism of growth by bulk diffusion.
|
-
15/2016 - 04/06/2016
Ieva, F.; Paganoni, A.M.
A taxonomy of outlier detection methods for robust classification in multivariate functional data | Abstract | | We propose a new method for robust classification of multivariate functional data. We exploit the joint use of two different depth measures, generalizing the outliergram to the multivariate functional framework, aiming at detecting and discarding both shape and magnitude outliers in order to robustify the reference samples of data, composed by G different known groups. We asses by means of a simulation study method’s performance in comparison with different outlier detection methods. Finally we consider
a real dataset: we classify a data minimizing a suitable distance from the
center of reference groups. We compare performance of supervised classification on test sets training the algorithm on original dataset and on the robustified one, respectively. |
-
14/2016 - 03/18/2016
Bonomi, D.; Manzoni, A.; Quarteroni, A.
A matrix discrete empirical interpolation method for the efficient model reduction of parametrized nonlinear PDEs: application to nonlinear elasticity problems | Abstract | | When using Newton iterations to solve nonlinear parametrized PDEs in the context of Reduced Basis (RB) methods, the assembling of the RB arrays in the online stage depends in principle on the high-fidelity approximation.
This task is even more challenging when dealing with fully nonlinear problems, for which the global Jacobian matrix has to be entirely reassembled at each Newton step.
In this paper the Discrete Empirical Interpolation Method (DEIM) and its matrix version MDEIM are exploited to perform system approximation at a purely algebraic level, in order to evaluate both the residual vector and the Jacobian matrix very efficiently. We compare different ways to combine solution-space reduction and system approximation, and we derive a posteriori error estimates on the solution accounting for the contribution of DEIM/MDEIM errors.
The capability of the proposed approach to generate accurate and efficient reduced-order models is demonstrated on the solution of two nonlinear elasticity problems. |
|
