Scientific Reports
The preprint collection of the Department of Mathematics.
Full-text generally not available for preprints prior to may 2006.
Found 866 products
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QDD111 - 11/24/2011
Antunes, P.; Gazzola, F.
Convex shape optimization for the least biharmonic Steklov eigenvalue | Abstract | | The least Steklov eigenvalue d1 for the biharmonic operator in bounded domains gives a bound for the positivity preserving property for the hinged plate problem, appears as a norm of a suitable trace operator, and gives the optimal constant to estimate the L2-norm of harmonic functions. These applications suggest
to address the problem of minimizing d1 in suitable classes of domains. We survey the existing results and conjectures about this topic; in particular, the existence of a convex domain of fixed measure minimizing d1 is known, although the optimal shape is still unknown. We perform several numerical experiments which strongly suggest that the optimal planar shape is the regular pentagon. We prove the existence of a domain minimizing d1 also among convex domains having fixed perimeter and present some numerical results supporting the conjecture that, among planar domains, the disk is the minimizer. |
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QDD110 - 11/21/2011
Guatteri, G.; Masiero F.
On the existence of optimal controls for SPDEs with boundary-noise and boundary-control | Abstract | | We consider a stochastic optimal control problem for an heat equation with boundary noise and boundary controls. Under suitable assumptions on the coefficients, we prove existence of optimal controls in strong sense by solving the stochastic hamiltonian system related. |
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QDD109 - 10/19/2011
Causin, P.; Sacco, R.; Verri, M.
In vitro tissue growth: a multiscale computational model of the dynamically evolving biophysical environment | Abstract | | Tissue Engineering (TE) is a field at the crossroad between Medicine, Life Sciences and Engineering, aimed at understanding the principles of tissue growth, and applying them to produce biologically functional replacements for clinical use. To achieve such an ambitious goal, complex biophysical phenomena must be mastered and related to the appropriate environment (nutrient delivery, fluid-mechanical loading and structural support) to be provided to cells. The TE problem is inherently multiphysics/multiscale, as it is characterized by material heterogeneities and interplaying processes occurring within a wide range of temporal and spatial scales. The concept we pursue in this paper is to use computational modelling of the TE problem to gain a quantitative and comprehensive understanding of phenomena often difficult to be
accessed experimentally. The present model represents, to our knowledge, the first example of a self-consistent high-resolution description of coupled nutrient mass transport, fluid-dynamics
and biomass production in TE constructs. We specifically focus on articular cartilage regeneration based on dynamically perfused
bioreactors and we investigate three issues critical in this application. First, we study oxygen distribution in the construct, since achieving an optimal level throughout the construct is a main tool to improve tissue quality. Second, we provide a quantitative evaluation on how interstitial perfusion can enhance nutrient delivery and, ultimately, biomass production, compared to static culture.
Third, we perform a sensitivity analysis with respect to biophysical parameters related to matrix production, assessing their rolein tissue regeneration.
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QDD108 - 10/05/2011
Dulio, P.; Peri, C.
INTERSECTING POLYTOPES AND TOMOGRAPHIC RECONSTRUCTIONS | Abstract | | In this paper we deal with the reconstruction problem in Tomography,
focusing on some new classes of subsets of the n-dimensional real space. Such classes are formed by clusters of polytopes mutually intersecting according to a twisting notion. The importance for tomography comes from their additivity property, which implies uniqueness of reconstruction. In the case n=2 we give a detailed description of their geometric structure, with some insight in the lattice frame. In particular, for a finite set D of directions in two-dimensional lattice, we introduce the class of D-inscribable lattice sets, showing that such sets can be considered as the natural discrete counterpart of the same notion known in the continuous case. Due to their nice tomographic properties, clusters of twisted polytopes might represent good candidates for approximating real shapes, as well as for investigating stability problems. |
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QDD107 - 09/23/2011
Barutello, V.; Terracini, S.; Verzini, G.
Entire minimal parabolic trajectories: the planar anisotropic Kepler problem | Abstract | | We continue the variational approach to parabolic tra jectories introduced in our previous paper [5], which sees parabolic orbits as minimal phase transitions.
We deepen and complete the analysis in the planar case for homogeneous singular potentials. We characterize all parabolic orbits connecting two minimal central configurations as free-time Morse minimizers (in a given homotopy class of paths). These may occur for at most one value of the homogeneity exponent. In addition, we link this threshold of existence of parabolic tra jectories with the absence of collisions for all the
minimizers of fixed-ends problems. Also the existence of action minimizing periodic trajectories with nontrivial homotopy type can be related with the same threshold. |
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QDD106 - 09/12/2011
Marazzina, D., Fusai, G.; Germano, G.
Pricing Credit Derivatives in a Wiener-Hopf Framework | Abstract | | We present fast and accurate pricing techniques for credit derivative contracts when discrete monitoring is applied and the underlying evolves according to an exponential L´evy process. Our pricing approaches are related to theWiener-Hopf factorization, and their computational cost is independent of the number of monitoring dates. Numerical results are presented in order to validate the pricing algorithm. Moreover, an analysis on the sensitivity of the probability of default and the credit spread term structures with respect to the process parameters is considered. |
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QDD105 - 07/20/2011
Frezzotti, A.; Ghiroldi, G.P.; Gibelli, L.
Solving Model Kinetic Equations on GPUs | Abstract | | We present an algorithm speci fically tailored for solving model kinetic equations
onto Graphics Processing Units (GPUs). The efficiency of the algorithm is demonstrated by solving the one-dimensional shock wave structure problem and the two-dimensional low Mach number driven cavity fl
ow. Computational results show that
it is possible to cut down the computing time of the sequential codes of two orders of
magnitude. The algorithm can be easily extended to more general collision models. |
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QDD104 - 07/13/2011
Elisabetta Maluta
A Class of P-convex Spaces Lacking Normal Structure | Abstract | | We consider a family of renormings of the infinite-dimensional separable Hilbert space introduced in literature by R.C. James in the sixties and prove that all its members are P-convex. It is known that these spaces lack normal structure when they are sufficiently far, in the sense of the Banach-Mazur distance, from being Hilbert, hence our result provides the first example of a P-convex space without normal structure. |
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