Quaderni MOX
Pubblicazioni
del Laboratorio di Modellistica e Calcolo Scientifico MOX. I lavori riguardano prevalentemente il campo dell'analisi numerica, della statistica e della modellistica matematica applicata a problemi di interesse ingegneristico. Il sito del Laboratorio MOX è raggiungibile
all'indirizzo mox.polimi.it
Trovati 1288 prodotti
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04/2014 - 26/01/2014
Palamara, S.; Vergara, C.; Catanzariti, D.; Faggiano, E.; Centonze, M.; Pangrazzi, C.; Maines, M.; Quarteroni, A.
Patient-specific generation of the Purkinje network driven by clinical measurements: The case of pathological propagations | Abstract | | To describe the electrical activity of the left ventricle is necessary to take into account the Purkinje fibers, responsible for the fast and coordinate ventricular activation, and their interaction with the muscular propagation. The aim of this work is to propose a methodology for the generation of a patient-specific Purkinje network driven by clinical measurements of the activation times acquired during pathological propagations. In particular, we consider clinical data acquired on four subjects suffering from pathologies with different origins, from conduction problems in the muscle or in the Purkinje fibers to a pre-excitation ventricular syndrome. To assess the accuracy of the proposed method, we compare the results obtained by using the patient-specific Purkinje network with the ones obtained by using a not patient-specific network. The results showed that the mean absolute errors are reduced by a factor in the range 27%-54%, highlighting the importance of including a patient-specific Purkinje network in computational models. |
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03/2014 - 25/01/2014
Kashiwabara, T.; Colciago, C.M.; Dede, L.; Quarteroni, A.
Well-posedness, regulariy, and convergence analysis of the Finite Element approximation of a Generalized Robin boundary value problem | Abstract | | In this paper, we propose the mathematical and finite element analysis of a second order Partial Differential Equation endowed with a generalized Robin boundary condition which involves the Laplace–Beltrami operator, by introducing a function space H 1 (Ω; Γ) of H 1 (Ω)-functions with H 1 (Γ)-traces, where Γ ⊆ ∂Ω. Based on a variational method, we prove that the solution of the generalized Robin boundary value problem possesses a better regularity property on the boundary than in the case of the standard Robin problem. We numerically solve generalized Robin problems by means of the finite element method with the aim of validating the theoretical rates of convergence of the error in the norms associated to the space H 1 (Ω; Γ).
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02/2014 - 23/01/2014
Antonietti, P.F.; Sarti, M.; Verani, M.
Multigrid algorithms for high order discontinuous Galerkin methods | Abstract | | In this paper we study the performance of a W-cycle multigrid algorithm for high order Discontinuous Galerkin discretizations of the Poisson problem. We recover the well known uniformity of the rate of convergence with respect to the mesh size and the number of levels and study the dependence on the polyonomial order p employed. The theoretical estimates are verified by two- and three-dimensional numerical tests. |
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01/2014 - 13/01/2014
Secchi, P.; Vantini, S.; Zanini, P.
Hierarchical Independent Component Analysis: a multi-resolution non-orthogonal data-driven basis | Abstract | | We introduce a new method, named HICA (Hierarchical Independent Component Analysis), suited to the dimensional reduction and the multi-resolution analysis of high dimensional and complex data. HICA solves a Blind Source
Separation problem by integrating Treelets with Independent Component Analysis and provides a multi-scale non-orthogonal data-driven basis apt
to meaningful data representations in reduced spaces. We describe some theoretical properties of HICA and we test the method on synthetic data. Finally, we apply HICA to the analysis of EEG traces. |
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67/2013 - 24/12/2013
Canuto, C.; Simoncini, V.; Verani, M.
On the decay of the inverse of matrices that are sum of Kronecker products | Abstract | | Decay patterns of
matrix inverses have recently attracted considerable interest,
due to their relevance in numerical analysis,
and in applications requiring matrix
function approximations.
In this paper we analyze the decay pattern of the inverse of banded matrices in the form
$S=M otimes I_n + I_n otimes M$ where $M$ is tridiagonal, symmetric and positive definite, $I_n$ is the identity matrix, and $ otimes$ stands for the Kronecker product.
It is well known that the inverses of banded matrices exhibit an exponential
decay pattern away from the main diagonal. However, the entries in $S^{-1}$
show a non-monotonic decay, which is not caught
by classical bounds. By using an alternative expression for $S^{-1}$, we
derive computable upper bounds that
closely capture the actual behavior of its entries. We also show that similar estimates
can be obtained when $M$ has a larger bandwidth, or when the sum of Kronecker
products involves two different matrices.
Numerical experiments illustrating the new bounds are also reported.
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66/2013 - 19/12/2013
Tricerri, P.; Dede ,L; Quarteroni, A.; Sequeira, A.
Numerical validation of isotropic and transversely isotropic constitutive models for healthy and unhealthy cerebral arterial tissues | Abstract | | This paper deals with the validation of constitutive models for healthy and unhealthy cerebral arterial tissues by means of numerical simulations of static inflation tests on a cylindrical geometry representing a specimen of anterior cerebral artery. The healthy arterial tissue is described by means of isotropic and transversely isotropic models. In particular, we validate a transversely isotropic multi-mechanism law, specifically proposed for the cerebral arterial tissue, for which the recruitment of the collagen fibers occurs at finite strains. Moreover, we consider numerical simulations of unhealthy cerebral arterial tissues by taking into account the mechanical weakening of the vessel wall that occurs during early development stages of cerebral aneurysms. We study the effects of the mechanical degradation on kinematic quantities of interest, namely the stresses distribution, that are commonly related to the progressive degradation of the arterial tissue by simulating static inflation tests for both isotropic and transversely isotropic models,
including the multi-mechanism law. |
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65/2013 - 17/12/2013
Ambrosi, D.; Ciarletta, P.
Plasticity in passive cell mechanics | Abstract | | A sufficiently large load applied to a living cell for a sufficiently long time produces a
deformation which is not entirely recoverable by passive mechanisms. This kind of plastic behavior is well documented by experiments but is still sel
dom investigated in terms of mechanical theories.
Here we discuss a finite visco-elasto-plastic
model where the rest elongation of the cell evolves in time as a function of the dissipated energy at a microstructural level. The theoretical predictions of the proposed model reproduce, also in quantitative terms, the passive mechanics of optically stretched cells. |
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64/2013 - 16/12/2013
Ciarletta, P; Ambrosi, D.; Maugin, G.A.
Mass transport in morphogenetic processes: a second gradient theory for volumetric growth and material remodeling | Abstract | | In this work, we derive a novel thermomechanical theory for growth and remodeling of biological materials in morphogenetic processes. This second gradient hyperelastic theory is the first attempt to describe both volumetric growth and mass transport phenomena in a single-phase continuum model, where both stress- and shape-dependent growth regulations can be investigated. The diffusion of biochemical species (e.g. morphogens, growth factors, migration signals) inside the material is driven by configurational forces, enforced in the balance equations and in the set of constitutive relations. Mass transport is found to depend both on first- and on second-order material connections, possibly withstanding a chemotactic behavior with respect to diffusing molecules. We find that the driving forces of mass diffusion can be written in terms of covariant material derivatives reflecting, in a purely geometrical manner, the presence of a (first-order) torsion and a (second-order) curvature.
Thermodynamical arguments show that the Eshelby stress and hyperstress tensors drive the rearrangement of the first- and second-order material inhomogeneities, respectively. In particular, an evolution law is proposed for the first-order transplant, extending a well-known
result for inelastic materials. Moreover, we define the first stress-driven evolution law of the second-order transplant in function of the completely material Eshelby hyperstress.
The theory is applied to two biomechanical examples, showing how an Eshelbian coupling
can coordinate volumetric growth, mass transport and internal stress state, both in physio-
logical and pathological conditions. Finally, possible applications of the proposed model are
discussed for studying the unknown regulation mechanisms in morphogenetic processes, as
well as for an optimizing scaffold architecture in regenerative medicine and tissue engineering. |
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