Scientific Reports
The preprint collection of the Department of Mathematics.
Full-text generally not available for preprints prior to may 2006.
Found 868 products
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QDD58 - 11/19/2009
Belhadji, L.; Bertacchi, D.; Zucca, F.
A self-regulating and patch subdivided population | Abstract | | We consider an interacting particle system on a graph which, from a macroscopic point of view,
looks like ${ mathbb Z}^d$ and, at a microscopic level, is a complete graph of degree $N$ (called a patch).
There are two birth rates: an inter-patch one $ lambda$ and an intra-patch one $ phi$. Once a
site is occupied, there is no breeding from outside the patch and the probability $c(i)$ of success of an intra-patch breeding decreases with the size $i$ of the population in the site. We prove the existence of a critical value $ lambda_{cr}( phi, c, N)$ and a critical value $ phi_{cr}( lambda, c, N)$.
We consider a sequence of processes generated by the families of control functions $ {c_i }_{i in N}$ and degrees $ {N_i }_{i in { mathbb N}}$; we prove, under mild assumptions, the existence of a critical value $i_{cr}( lambda, phi,c)$. Roughly speaking we show that, in the limit, these processes behave as the branching random walk on ${ mathbb Z}^d$ with intra-neighbor birth rate $ lambda$ and on-site birth rate $ phi$.
Some examples of models that can be seen as particular cases are given. |
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QDD54 - 11/06/2009
Berchio, E ; Gazzola, F.
Positive solutions to a linearly perturbed critical growth biharmonic problem | Abstract | | Existence and nonexistence results for positive solutions to a linearly perturbed critical growth biharmonic problem under Steklov boundary conditions, are determined. Furthermore, by investigating the critical dimensions for this problem, a Sobolev inequality with remainder terms, of both interior and boundary type, is deduced. |
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QDD55 - 10/14/2009
Fagnola, F.; Gregoratti, M.
Bell s Inequality Violations: Relation with de Finetti s Coherence Principle and Inferential Analysis of Experimental Data | Abstract | | It is often believed that de Finetti s coherence principle in the finite case naturally leads to the Kolmogorov s probability theory of random phenomena and that such a theory unavoidably implies Bell s inequality. Thus, an alternative probability theory allowing for a violation of Bell s inequality, such as quantum probability, should violate also de Finetti s coherence principle. Firstly, we show that this is not the case: the typical violations of Bell s inequality are in theoretical agreement with de Finetti s coherence principle. Secondly, we consider the experimental data of measurements of polarization of photons, performed to verify empirically violations of Bell s inequality. We analyze them to test the null hypothesis of validity of the Kolmogorov s probability model for the observed phenomenon and we compute their p-value to quantify the experimental violation of the null hypothesis. |
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QDD53 - 09/30/2009
de Falco, C.; Sacco, R.; Verri, M.
Analytical and Numerical Study of Photocurrent Transients in Nanoscale Organic Solar Cells | Abstract | | In this article, we deal with the mathematical
modeling and numerical simulation of photocurrent transients in nanoscale mono-layer Organic polymer Solar Cells (OSCs). The mathematical model consists of a system of non-linear diffusion-reaction partial differential equations (PDEs) with electrostatic convection, coupled to a kinetic ordinary differential equation (ODE).
We propose a suitable reformulation of the model
which makes it similar to the classical drift-diffusion system for inorganic semiconductor devices. This allows us, on the one hand, to prove the existence of a solution for the problem
in both stationary and transient conditions
and, on the other hand, to better highlight
the role of exciton dynamics in determining the device turn-on time. For the numerical treatment of the problem, we carry out a temporal semi-discretization using an implicit adaptive method, and the resulting sequence of differential subproblems is linearized using the Newton-Raphson method with inexact evaluation of the Jacobian. Then, we use exponentially fitted finite elements for the spatial discretization, and we carry out a thorough validation of the computational model by extensively investigating
the impact of the model parameters on photocurrent transient times.
A modified version of this paper will appear in Comp. Meth. Appl. Mech. Engrg. (2010)
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QDD51 - 09/23/2009
Carriero, M.; Leaci A.; Tomarelli F.
Variational approach to image segmentation | Abstract | | This paper focuses on a second order functional depending on free discontinuity and free gradient-discontinuity, whose minimizers provide a variational solution to contour detection problem in image segmentation.
We briefly resume the state of the art about
Blake & Zisserman functional under different types of boundary condition which are related to contour enhancement in image segmentation.
We prove a new Caccioppoli inequality suitable to study regularity of minimizers of related boundary value problems in any dimension $n ge 1$ and deduce that there are no nontrivial local minimizers in half-space. |
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QDD52 - 09/23/2009
Percivale D.; Tomarelli F.
Regular minimizers of some free discontinuity problems | Abstract | | We show that minimizers of free discontinuity problems with energy dependent on jump integrals and Dirichlet boundary conditions are smooth provided a smallness condition is imposed on data.
We examine several examples, including elastic-plastic beam and plate with free yield lines and deformable body with free damage. In all cases there is a gap between the condition for solvability (safe load condition) and this smallness condition (load regularity condition).
Such gap allows the existence of damaged/creased minimizers. Eventually we provide explicit examples of irregular solutions when the load stays in the gap. |
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QDD46 - 07/15/2009
Bertacchi, D. ; Posta, G. ; Zucca, F.
Ecological equilibrium for restrained branching random walks | Abstract | | We study a generalized branching random walk where particles breed at a rate which depends on the number of neighbouring particles.
Under general assumptions on the breeding rates we prove the existence of a phase where the population survives without exploding.
We construct a non trivial invariant measure for this case. |
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QDD47 - 07/15/2009
Zucca, F.
An inequality for correlated measurable functions | Abstract | | A classical inequality, which is known for families of monotone functions, is generalized to a larger class of families of measurable functions. Moreover we characterize all the families of functions for which the equality holds. We give two applications of this result, one of them to a problem arising from probability theory. |
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