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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QDD19 - 05/28/2007
Percivale, D.; Tomarelli F.
A variational principle for plastic hinges in a beam | Abstract | | We focus the minimization of 1D free discontinuity problem with second order energy dependent on jump integrals but not on the cardinality of the discontinuity set, in the framework of $L^ infty$ load. The related energies are not lower semi continuous in $BH$. Nevertheless we show that if a safe load condition is fulfilled then minimizers exist and they belong actually to $SBH,$ say their second derivative has no Cantor part. If in addition a stronger condition on load is fulfilled then
minimizer is unique and belongs to $H^2$. Moreover we can always select one minimizer whose number of plastic hinges does not
exceed 2 and is the limit of minimizers of penalized problems.
When the load stays in the gap between safe load and regularity condition then minimizers with hinges are allowed; if in addition the load is symmetric and strictly positive then there
is uniqueness of minimizer, the hinges of such minimizer are exactly two and they are located at the endpoints.
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QDD18 - 04/17/2007
Pierotti, D. ; Simioni, P.
The steady two-dimensional flow over a rectangular obstacle lying on the bottom | Abstract | | We study a plane problem with mixed boundary conditions for a harmonic function in an unbounded Lipschitz domain contained in a strip. The problem is obtained by linearizing the hydrodynamic equations which describe the steady flow of a heavy ideal fluid over an obstacle lying on the flat bottom of a channel. In the case of obstacles of rectangular shape we prove unique solvability for all velocities of the (unperturbed) flow above a critical value depending on the obstacle depth. We also discuss regularity and asymptotic properties of the solutions. |
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QDD17 - 03/26/2007
Longaretti, M.; Chini, B.; Jerome, J.W.; Sacco, R.
Electrochemical Modeling and Characterization of Voltage Operated Channels in Nano-Bio-Electronics | Abstract | | In this article, the electrical characterization of Voltage Operated ionic Channels (VOCs) in Nano-Bio-Electronics applications is carried out.
This is one of the relevant steps towards a multi-physics description of hybrid bio-electronical devices such as bio-chips.
Electrochemical ionic transport phenomena are properly modeled by a Poisson-Nernst-Planck partial differential system of nonlinearly coupled equations, while suitable functional iteration techniques for problem decoupling and finite element methods for discretization are proposed and discussed. Extensive numerical simulations of
single species VOCs transporting $K^+$ ions
are performed to consistently derive an electrical equivalent representation of the channel and to quantitatively describe its interaction with an external measurement device under several working conditions. |
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QDD16 - 02/27/2007
Rizzi, Cecilia
Infinitesimal invariant and Massey products | Abstract | | In this work, we study the Griffths infinitesimal invariant of the curve in the jacobian using
secondary cohomology maps. In order to this, we construct a special differential graded algebra
A, quite similar to the Kodaira-Spencer algebra and we define a natural triple Massey product
on it. This allows us to give a description of the infinitesimal invariant in terms of Massey
products and, by the way, to study the formality of A. |
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QDD15 - 02/26/2007
Gregoratti, M.
Classical dilations a la Hudson-Parthasarathy of Markov semigroups | Abstract | | We study the Classical Probability analogue of the dilations of a quantum dynamical semigroup defined in Quantum Probability via quantum stochastic differential equations. Given a homogeneous Markov chain in continuous time in a finite state space E, we introduce a second system, an environment, and a deterministic invertible time-homogeneous global evolution of the system E with this environment such that the original Markov evolution of E can be realized by a proper choice of the initial random state of the environment.
We also compare this dilations with the dilations of a quantum dynamical semigroup in Quantum Probability: given a classical Markov semigroup,
we extend it to a proper quantum dynamical semigroup for which we can find a Hudson-Parthasarathy dilation which is itself an extension of our classical dilation. |
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QDD14 - 02/22/2007
Gregoratti, M.
Classical Dilations a la Quantum Probability of Markov Evolutions in discrete time | Abstract | | We study the Classical Probability analogue of the dilations of a quantum dynamical semigroup in Quantum Probability. Given a (not necessarily homogeneous) Markov chain in discrete time in a finite state space $E$, we introduce a second system, an environment, and a deterministic invertible time-homogeneous global evolution of the system $E$ with this environment such that the original Markov evolution of $E$ can be realized by a proper choice of the initial random state of the environment. We also compare this dilations with the dilations of a quantum dynamical semigroup in Quantum Probability: given a classical Markov semigroup, we show that it can be extended to a quantum dynamical semigroup for which we can find a quantum dilation to a group of $*$-automorphisms admitting an invariant abelian subalgebra where this quantum dilation gives just our classical dilation. |
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QDD13 - 02/15/2007
El-Shanawany R. A. ; Higazy M. Sh. ; Scapellato R.
Orthogonal Double Covers of Complete Bipartite Graphs by Symmetric Starters | Abstract | | Let H be a graph on n vertices and C a collection of n subgraphs of H, one for each vertex. Then C is an orthogonal double cover (ODC) of H if every edge of H occurs in exactly two members of C and any two members of C share exactly an edge whenever the corresponding vertices are adjacent in H. If all subgraphs in C are isomorphic to a given graph G, then C is said to be an ODC of H by G.
We construct the ODCs of the complete bipartite graph with two classes of n vertices by a
graph G which is the union of a m-path and
a (n-m)-star, where the center of the star is a one of the path ends, for all m=5,6,7,8,9,10. In all cases, G is a symmetric starter of the cyclic group of order n. |
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QDD12 - 01/03/2007
Pierotti, D.
On the plane problem of the flow around a submerged beam | Abstract | | We consider the problem of the steady flow of an ideal heavy fluid around a submerged beam. The problem is obtained from the free-boundary problem of the flow past a submerged obstacle in the limit of bodies of vanishing thickness. We introduce a special Sobolev space formulation of the problem in term of a perturbed stream function and prove its unique solvability for every value of the unperturbed flow velocity, with the possible exception of a discrete set depending on the geometry of the domain. The asymptotic properties of the solutions are discussed. |
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