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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61/2014 - 12/16/2014
Taffetani, M.; Ciarletta, P.
Elasto-capillarity controls the formation and the morphology of beads-on-string structures in solid fibres | Abstract | | Beads-on-string patterns have been experimentally observed in solid cylinders for a wide range of material properties and structural lengths, from millimetric soft gels to nanometric hard fibres. In this work, we combine theoretical analysis and numerical tools to investigate the formation and the nonlinear dynamics of such beaded structures. We show that this morphological transition is driven by elasto-capillarity, i.e. a complex interplay between the effects of surface tension and bulk elasticity. Unlike buckling or wrinkling, the presence of an axial elongation is found here to favour the onset of fibre beading, in agreement with existing experimental results on electrospun fibres, hydrogels and nerves. Our results also prove that the applied stretch can be used in fabrication techniques to control the morphology of the emerging beads-on-string patterns. Such quantitative predictions open the way to several applications, from tissue engineering to the design of stretchable electronics and the micro-fabrication of functionalized surfaces. |
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57/2014 - 12/12/2014
Giverso, C.; Verani, M.; Ciarletta P.;
Branching instability in expanding bacterial colonies | Abstract | | Self-organization in developing living organisms relies on the capability of cells to duplicate and perform a collective motion inside the surrounding environment.
Chemical and mechanical interactions coordinate such a cooperative behavior, driving the dynamical evolution of the macroscopic system. In this work, we perform an analytical and computational analysis to study pattern formation during the spreading of an initially circular bacterial colony on a Petri dish. The continuous
mathematical model addresses the growth and the chemotactic migration of the living monolayer, together with the diffusion and consumption of nutrients in the agar. The governing equations contain four dimensionless parameters, accounting for the interplay among the chemotactic response, the bacteria-substrate
interaction and the experimental geometry. The spreading colony is found to be always linearly unstable to perturbations of the interface, whilst branching instability arises in finite-element numerical simulations. The typical length-scales of such fingers, which align in the radial direction and later undergo further branching, are controlled by the size parameters of the problem, whilst the emergence of branching is favored if the diffusion is dominant on the chemotaxis. The model is able to predict the experimental morphologies and their dynamical evolution,
confirming that compact (resp. branched) patterns arise for fast (resp. slow) expanding colonies. Such results, while providing new insights on pattern selection in bacterial colonies, may finally have important applications for designing controlled patterns. |
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58/2014 - 12/12/2014
Menafoglio, A.; Secchi, P.; Guadagnini, A.
A Class-Kriging predictor for Functional Compositions with Application to Particle-Size Curves in Heterogeneous Aquifers | Abstract | | We address the problem of characterizing the spatial field of soil particle-size curves (PSCs) within a heterogeneous aquifer system. We conceptualize the medium as a composite system, associated with an uncertain spatial arrangement of geomaterials. We tie the identification of the latter to the spatially varying arrangement of soil textural properties, which is in turn estimated by an available set of observed PSCs. We analyze these PSCs through their particle-size densities (PSDs), which are interpreted as points in the infinite-dimensional Hilbert space of functional compositions (FCs). To model the heterogeneity of the system, we introduce an original hierarchical model for FCs, conducive to a Functional Compositional Class-Kriging (FCCK) predictor. To tackle the problem of lack of information when the spatial arrangement of soil types is unobserved, we propose a novel clustering method for spatially dependent FCs. The latter allows inferring a grouping structure from sampled PSDs, consistent with our theoretical framework. This enables one to project the complete information content embedded in the set of heterogenous PSDs to unsampled locations in the system, thus providing predictions of the spatial arrangement of (a) regions associated with each identified textural class, and (b) the PSDs within each region. Our methodological developments are tested on a field application relying on a set of particle-size curves observed within an alluvial aquifer in the Neckar river valley, in Germany. |
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59/2014 - 12/12/2014
Manzoni, A.; Pagani, S.; Lassila, T.
Accurate solution of Bayesian inverse uncertainty quantification problems using model and error reduction methods | Abstract | | Computational inverse problems related to partial differential equations (PDEs) often contain nuisance parameters that cannot be effectively identified but still need to be considered as part of the problem. The objective of this work is to show how to take advantage of projection-based reduced order models (ROMs) to speed up Bayesian inversion on the identifiable parameters of the system, while marginalizing away the (potentially large number of) nuisance parameters. The key ingredients are twofold. On the one hand, we rely on a reduced basis (RB) method, equipped with computable a posteriori error bounds, to speed up the solution of the forward problem. On the other hand, we develop suitable reduction error models (REM) to quantify the error between the full-order and the reduced-order model affecting the likelihood function, in order to gauge the effect of the ROM on the posterior distribution of the identifiable parameters. Numerical results dealing with inverse problems governed by elliptic PDEs in the case of both scalar parameters and parametric fields highlight the combined role played by ROM accuracy and REM effectivity. |
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60/2014 - 12/12/2014
Signorini, M.; Micheletti, S.; Perotto, S.
CMFWI: Coupled Multiscenario Full Waveform Inversion for seismic inversion | Abstract | | We present the new method Coupled Multiscenario Full Waveform Inversion (CMFWI) for the solution of the seismic inversion problem. As in the case of Full Waveform Inversion (FWI), the proposed method is based on seismic reflection signals and it tries to recover the subsoil velocity profile by minimizing a suitable misfit functional between recorded and computed data. CMFWI suitably combines data generated by shooting one source at a time, but sharing the effect of this signal with the other sources. Moreover, CMFWI differs from FWI employed with the same sources shot together, and we numerically show that it performs better than FWI. In particular, this comparison focuses on different types of boundary conditions, wave sources, initial guesses of the velocity profile, and signal-to-noise ratio.
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55/2014 - 12/02/2014
Antonietti, P. F.; Houston P.; Sarti, M.; Verani, M.
Multigrid algorithms for hp-version Interior Penalty Discontinuous Galerkin methods on polygonal and polyhedral meshes | Abstract | | In this paper we analyze the convergence properties of two-level and W-cycle multigrid solvers for the numerical solution of the linear system of equations arising from hp-version symmetric interior penalty discontinuous Galerkin discretizations of second-order elliptic partial differential equations on polygonal/polyhedral meshes. We prove that the two-level method converges uniformly with respect to the granularity of the grid and the polynomial approximation degree p, provided that the number of smoothing steps, which depends on p, is chosen sufficiently large. An analogous result is obtained for the W-cycle multigrid algorithm, which is proved to be uniformly convergent with
respect to the mesh size, the polynomial approximation degree, and the number of levels, provided the latter remains bounded
and the number of smoothing steps is chosen sufficiently large. Numerical experiments are presented which underpin the theoretical predictions; moreover, the proposed multilevel solvers are shown to be convergent in practice, even when some of the theoretical assumptions are not fully satisfied. |
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56/2014 - 12/02/2014
Antonietti, P. F.; Sarti, M.; Verani, M.; Zikatanov, L. T.
A uniform additive Schwarz preconditioner for the hp-version of Discontinuous Galerkin approximations of elliptic problems | Abstract | | In this paper we design and analyze a uniform preconditioner for a class of high order Discontinuous Galerkin schemes. The preconditioner is based on a space splitting involving the high order conforming subspace and
results from the interpretation of the problem as a nearly-singular problem. We show that the proposed preconditioner exhibits spectral bounds that are uniform with respect to the discretization parameters, i.e., the mesh size, the polynomial degree and the penalization coefficient. The theoretical estimates obtained are supported by several numerical simulations. |
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54/2014 - 11/28/2014
Ferrario, E.; Pini, A.
Uncertainties in renewable energy generation systems: functional data analysis, monte carlo simulation, and fuzzy interval analysis | Abstract | | In this paper, aleatory and epistemic uncertainties in energy generation systems are investigated. The former are described by probability distributions, whereas the latter by possibility distributions. In particular, time-varying probability distributions elicited by Functional Data Analysis are considered for the representation of the aleatory uncertainty that evolves with time. Then, the joint propagation of both types of uncertainty is performed by Monte Carlo simulation and Fuzzy Interval Analysis. The method is applied to a model of an energy system made of a solar panel, a storage energy system and the loads. As a quantitative indicator of the analysis we evaluate the Expected Energy Not Supplied. |
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