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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64/2013 - 12/16/2013
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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63/2013 - 12/05/2013
Pigoli, D.; Menafoglio, A.; Secchi, P.
Kriging prediction for manifold-valued random field | Abstract | | The statistical analysis of data belonging to Riemannian manifolds is becoming increasingly important in many applications, such as shape analysis, diffusion tensor imaging and the analysis of covariance matrices. In many cases, data are spatially distributed but it is not trivial to take into account spatial dependence in the analysis because of the non linear geometry of the manifold. This work proposes a solution to the problem of spatial prediction for manifold valued data, with a particular focus on the case of positive definite symmetric matrices. Under the hypothesis that the dispersion of the observations on the manifold is not too large, data can be projected on a suitably chosen tangent space, where an additive model can be used to describe the relationship between response variable and covariates. Thus, we generalize classical kriging prediction, dealing with the spatial dependence in this tangent space, where well established Euclidean methods can be used. The proposed kriging prediction is applied to the matrix field of covariances between temperature and precipitation in Quebec, Canada. |
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62/2013 - 12/01/2013
Arioli, G.; Koch, H.
Existence and stability of traveling pulse solutions of the FitzHugh-Nagumo equation | Abstract | | The FitzHugh-Nagumo model is a reaction-diffusion equation describing the propagation of electrical signals in nerve axons and other biological tissues. One of the model parameters is the ratio epsilon of two time scales, which takes values between 0.001 and 0.1 in typical simulations of nerve axons. Based on the existence of a (singular) limit at epsilon = 0, it has been shown that the FitzHugh-Nagumo equation admits a stable traveling pulse solution for sufficiently small epsilon > 0. In this paper we prove the existence of such a solution for epsilon = 0.01. We consider both circular axons and axons of infinite length. Our method is non-perturbative and should apply to a wide range of other parameter values.
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61/2013 - 11/30/2013
Antonietti, P.F.; Sarti, M.; Verani, M.
Multigrid algorithms for hp-Discontinuous Galerkin discretizations of elliptic problems | Abstract | | We present W-cycle multigrid algorithms for the solution of the linear system of equations arising from a wide class of hp-version discontinuous Galerkin discretizations of elliptic problems. Starting from a classical framework in multigrid analysis, we define a smoothing and an approximation property, which are used to prove the uniform convergence of the W-cycle scheme with respect to the granularity of the grid and the number of levels. The dependence of the convergence rate on the polynomial approximation degree p is also tracked, showing that the contraction factor of the scheme deteriorates with increasing p. A discussion on the effects of employing inherited or non-inherited sublevel solvers is also presented. Numerical experiments confirm the theoretical results. |
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60/2013 - 11/29/2013
Ghiglietti, A.; Paganoni, A.M.
An urn model to construct an efficient test procedure for response adaptive designs | Abstract | | We study statistical performance of different tests for comparing the mean effect of two treatments. Given a test T0, we determine which sample size and proportion allocation guarantee to a test T to be better than T0, in terms of (a) higher power and (b) fewer subjects assigned to the inferior treatment. The adoption of a response adaptive design to implement the random allocation procedure is necessary to ensure that both (a) and (b) are satisfied. In particular, we propose to use a Modified Randomly Reinforced Urn design (MRRU) and we show how to perform the model parameters selection for the purpose of this paper. The opportunity of relaxing some assumptions is examined. Results of simulation studies on the test performance are reported and a real case study is analyzed. |
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59/2013 - 11/25/2013
Aletti, M.; Bortolossi, A.; Perotto, S.; Veneziani, A.
One-dimensional surrogate models for advection-diffusion problems | Abstract | | Numerical solution of partial differential equations can be made more tractable
by model reduction techniques. For instance, when the problem at hand presents
a main direction of the dynamics (such as blood flow in arteries), it may be
conveniently reduced to a 1D model. Here we compare two strategies to obtain this
model reduction, applied to classical advection-diffusion equations in domains
where one dimension dominates the others. |
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58/2013 - 11/20/2013
Artina, M.; Fornasier, M.; Micheletti, S.; Perotto, S.
Anisotropic adaptive meshes for brittle fractures: parameter sensitivity | Abstract | | We deal with the Ambrosio-Tortorelli approximation of the well-known Mumford-Shah functional to model quasi-static crack propagation in brittle materials.
We employ anisotropic mesh adaptation to efficiently capture the crack path.
Aim of this work is to investigate the numerical sensitivity
of the crack behavior to the parameters involved in both the physical model
and in the adaptive procedure. |
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57/2013 - 11/17/2013
Antonietti, P.F.; Perugia, I.; Zaliani, D.
Schwarz domain decomposition preconditioners for plane wave discontinuous Galerkin methods | Abstract | | We construct Schwarz domain decomposition preconditioners for plane wave discontinuous Galerkin methods for Helmholtz boundary value problems. In particular, we consider additive and multiplicative non-overlapping Schwarz methods. Numerical tests show good performance of these preconditioners when solving the linear system of equations with GMRES. |
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