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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21/2009 - 08/20/2009
Bonaventura, Luca; Castruccio, Stefano; Sangalli, Laura M.
A Bayesian approach to geostatistical interpolation with exible variogram models | Abstract | | A Bayesian approach to covariance estimation and geostatistical interpolation based on flexible variogram models is introduced. In particular,
we consider black-box kriging models. These variogram models do not require restrictive assumptions on the functional shape of the variogram; furthermore, they can handle quite naturally non isotropic random fields.
The proposed Bayesian approach does not require the computation of an empirical variogram estimator, thus avoiding the arbitrariness implied by the construction of the empirical variogram itself. Moreover, it provides a complete assessment of the uncertainty in the variogram estimation. The advantages of this approach are illustrated via an extensive simulation study and by application to a well known benchmark dataset. |
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20/2009 - 07/25/2009
Accoto, Nadia; Rydén, Tobias; secchi, Piercesare
Bayesian hidden Markov models for performance-based regulation of continuity of electricity supply | Abstract | | A fundamental aspect in the regulation of continuity of electricity supply is the identification of faults that could be caused by an exceptional event and therefore that are outside the utility control and responsibility.
Different methods have been proposed during the years; the interpretation of the observed faults as a signal of an underlying system naturally leads to the analysis of the problem by means of an hidden Markov model. These models, in fact, are widely used for introducing dependence in data and/or for modelling observed phenomena depending on hidden processes. The application of this method shows that the model is able to identify exceptional events; moreover the study of the estimated model parameters gives rise to reality-linked considerations. |
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19/2009 - 07/24/2009
Formaggia, Luca; Mola, Andrea; Parolini, Nicola; Pischiutta, Matteo
A three-dimensional model for the dynamics and hydrodynamics of rowing boats | Abstract | | This paper proposes a new model describing the dynamics of a rowing boat for general three dimensional motions. The complex interaction among the different components of the rowers/oars/boat system is analysed and reduced to a set of ordinary differential equations governing the rigid motion along the six degrees of freedom. To treat the unstable nature of the physical problem, a rather simple (but effective) control model is included, which mimics the main active control techniques adopted by the rowers during their action. |
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18/2009 - 07/23/2009
Silva Soares, Joao; Zunino, Paolo
A mathematical model for water uptake, degradation, erosion and drug release from degradable polydisperse polymeric networks | Abstract | | We introduce a general class of mixture models to study water uptake, degradation, erosion, and drug release from degradable polydisperse polymeric matrices.
The mathematical model is based on a finite number of constituents describing the polydisperse polymeric system, i.e. each representing collection of chains whose size
belongs to a finite interval of degree of polymerization. In order to model water uptake
and drug release, two additional constituents (water and drug) constitute the mixture.
Constituents diffuse individually accordingly to Fick’s first law and balances of mass of constituents yield partial differential equations that govern the reaction-diffusion system. Hydrolysis, a chemical reaction that breaks down larger chains into smaller ones, is accounted with reactions terms quantifying sources and sinks of polymeric chains and a sink of water. Hydrolysis couples the system of equations and nonlinearities appear through constitutive specification of the diffusivities of constituents on the current network, reaction rates, and boundary conditions.
The mathematical model is independent of the number of constituents describing the polydisperse polymeric system and hydrolysis kinetics describe with accuracy the overall decrease in molecular weight distribution and satisfies a monomer conservation principle. A shift between two different types of solutions of the system of partial differential equations, each identified to surface or bulk erosion, is obtained with the variation of a single non-dimensional number, the Thiele modulus, which measures the relative importance of the mechanisms of reaction and diffusion. Results of drug release confirm that drug release from bulk eroding matrices is diffusion-controlled, whereas for surface eroding polymers, drug release is enhanced in an erosion-controlled process. |
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17/2009 - 06/18/2009
Longoni, Matteo; Magistroni, Corrado; Ruffo, Paolo; Scrofani, Giovanni
3D Inverse and Direct Structural modeling Workflow | Abstract | | The description and the interpretation of the geological evolution of sedimentary basins has recently received a great support from the use of
mathematical models and numerical methods, taking advantage of more advanced hardware, both in graphic and computing power. We have developed a geological modeling workflow, based on gOcad, for the 3D inverse and direct structural modeling of sedimentary basins. The workflow is based on an appropriate number of time-steps of restoration modeling coupled with forward/evolution modeling. During each step a gOcad geological model provides support for data managing, pre- and post-processing for numerical solvers and the necessary interpretative model editing.
The capability of capturing and describing all the geometrical and structural features of an accurate geological model, leads to remarkable results in integrating available data, in validating restoration models and in reconstructing a reliable evolution of a basin.
The model is built with gOcad, starting from the basin geometrical data. Topological complexities such as faulted stratified layers and salt
diapirs are easily handled in a three-dimensional unstructured framework.
Then the geometrical model is enriched with its physical properties, coming from seismic, well and field data and from the modeller conceptual model. The domain is then described with a user-defined tetrahedral mesh, necessary for the numerical simulation of its geological evolution. The output results, for example the updated position of horizon and fault surfaces, and
the distributions in the domain of physical quantities such as stresses and displacements, are then imported in gOcad by means of a fully-automatic procedure, for data visualization and analysis. The workflow can be iterated starting from the last updated configuration.
We present the application of the workflow to the simulation of the dynamic structural evolution in two realistic cases: a multi-faulted system
and a diapir growth in a multi-layered sedimentary basin.
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16/2009 - 05/20/2009
Aletti, Giacomo; May, Caterina; Secchi, Piercesare
A functional equation whose unknown is P ([0, 1]) valued | Abstract | | We study a functional equation whose unknown maps a euclidean space into the space of probability distributions on [0,1].
We prove existence and uniqueness of its solution under suitable regularity and boundary conditions and we characterize solutions that are diffuse on [0,1]. A canonical solution is obtained by means
of a Randomly Reinforced Urn with different reinforcement distributions having equal means. |
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15/2009 - 05/07/2009
Perotto, Simona; Ern, Alexandre; Veneziani, Alessandro
Hierarchical local model reduction for elliptic problems I: a domain decomposition approach | Abstract | | Some engineering applications, for instance related to fluid dynamics in pipe or channel networks, feature a dominant spatial direction along which the most relevant dynamics develop. Nevertheless, local features of the problem depending on the other directions, that we call transverse, can be locally relevant to the whole problem. We propose in the context of ellip-
tic problems such as advection–diffusion–reaction equations, a hierarchical model reduction approach in which a coarse model featuring only the dominant direction dynamics is enriched locally by a fine model that accounts for the transverse variables via an appropriate modal expansion. We introduce a domain decomposition approach allowing us to employ a different
number of modal functions in different parts of the domain according to the local complexity of the problem at hand. The methodology is investigated numerically on several test cases. |
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14/2009 - 04/08/2009
Beirao da Veiga, Lourenco; Verani, Marco
A posteriori boundary control for FEM approximation of elliptic eigenvalue problems | Abstract | | We derive new a posteriori error estimates for the nite element solution of an elliptic eigenvalue problem, which take into account also the e ects of the polygonal approximation of the domain. This suggests local error indicators that can be used to drive a procedure handling the mesh re nement together with the approximation of the domain. |
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