Scientific Reports
The preprint collection of the Department of Mathematics.
Full-text generally not available for preprints prior to may 2006.
Found 866 products
-
QDD11 - 12/19/2006
Guatteri, G.; Tessitore, G.
Backward Stochastic Riccati Equations and Infinite Horizon L-Q Optimal Control with Infinite Dimensional State Space and Random Coefficients | Abstract | | We study the Riccati equation (BSRE) arising in a class of quadratic optimal control problems with
infinite dimensional stochastic differential state equation and infinite horizon cost functional. We allow the coefficients, both in the state equation and in the cost, to be random.
In such a context BSREs are backward stochastic differential equations in the whole positive real axis that involve quadratic non-linearities and take values in a non-Hilbertian space. We prove existence of a minimal non-negative solution and, under additional assumptions, its uniqueness. We show that such a solution allows to perform the synthesis of the optimal control and investigate its
attractivity properties. Finally the case where the coefficients are stationary is addressed and an example concerning a controlled wave equation in random media is proposed. |
-
QDD10 - 12/18/2006
Carriero, M.; Leaci, A.; Tomarelli, F.
Candidate local minimizer of Blake & Zisserman functional (Appendix to QDD 9 (Euler equations for Blake & Zisserman functional)) | Abstract | | Almansi decomposition and explicit coefficients of asymptotic expansion around the origin for bi-harmonic functions in a disk with a crack are evaluated by simbolic computations with Mathematica 5.0 .
We deduce S.I.F. and modes coefficients of the leading term in the expansion for candidate local minimizer of Blake & Zisserman functional. |
-
QDD9 - 12/13/2006
Carriero, M. ; Leaci, A. ; Tomarelli, F.
Euler equations for Blake & Zisserman functional | Abstract | | We derive many necessary conditions for
minimizers of a functional depending on free discontinuities, free gradient discontinuities and second derivatives, which is related
to image segmentation.
A candidate for minimality of main part
of the functional is explicitly exhibited. |
-
QDD8 - 11/30/2006
Barchielli, A.; Lupieri, G.
Information gain in quantum continual measurements | Abstract | | Inspired by works on information transmission through quantum channels, we propose the use of a couple of mutual entropies to quantify the efficiency of continual measurement schemes in extracting information on the measured quantum system. Properties of these measures of information are studied and bounds on them are derived. |
-
QDD6 - 11/07/2006
Causin, P.; Sacco, R.
Static condensation procedures for hybridized mixed finite element methods | Abstract | | Stemming from the characterization of the static condensation procedure for mixed hybridized methods introduced in [9],[10], in this paper
we use Helmholtz decompositions to obtain a substructuring of the local mapping problems, in order to end up with simpler systems of reduced size. This procedure is effective especially when dealing with high degree or variable degree
approximations. Moreover, we extend the variational characterization of static condensation
to more general saddle-point formulations.
Two relevant examples of hybridized mixed methods are considered, namely, the classical Galerkin Dual-Mixed Hybridized scheme and the Discontinuous Petrov-Galerkin (DPG) scheme of [7]. |
-
QDD7 - 11/07/2006
Longaretti, M.; Marino, G.; Chini, B.; Jerome, J.W.; Sacco, R.
Computational models in nano-bio-electronics: simulation of ionic transport in voltage operated channels | Abstract | | In this article, a novel mathematical and computational model is proposed for the
numerical simulation of Voltage Operated ionic Channels (VOC) in Nano-Bio-Electronics applications.
This is a first step towards a multi-physics description of hybrid bio-electronical devices such as bio-chips.
The model consists of a coupled system of nonlinear partial differential equations, comprising a Poisson-Nernst-Planck system to account for electro-chemical phenomena, and a Navier-Stokes system to account for fluid-mechanical phenomena.
Suitable functional iteration techniques for problem decoupling and finite element methods for discretization are proposed and discussed. Numerical results on realistic VOCs illustrate the validity of the model and its accuracy by comparison with relevant computed channel equivalent electrical parameters with measured data. |
-
QDD4 - 10/13/2006
Bouchitte, G. ; Fragala, I.
Optimal design of thin plates by a dimension reduction for linear constrained problems | Abstract | | Our main goal is to give a rigorous justification
for the Hessian-constrained problems introduced in [*] and to show how they are linked to the optimal design of thin plates.
To that aim, we study the asymptotic behaviour of a sequence of optimal elastic compliance problems, in the double limit when both the maximal height of the design region and the total volume of the material tend to zero. In the vanishing volume limit, a sequence of linear constrained first order vector problems is obtained, which in turn - in the vanishing thickness limit - produces a new linear constrained problem where both first and
second order gradients appear. When the load is suitably chosen, only the Hessian constraint is active, and we recover exactly the plate optimization problem studied in [*]. Some attention
is also paid to the possible different approaches to the afore mentioned double limit process, in both the cases of real and ficticious materials, which might favour some debate on the modelling of thin plates.
[*] Bouchitte, G. ; Fragala, I.
Optimality conditions for mass design problems and applications to thin plates. Arch. Rat. Mech. Analysis, to appear.
|
-
QDD3 - 10/02/2006
Barchielli, A.
Some stochastic differential equations in quantum optics and measurement theory: the case of counting processes | Abstract | | Stochastic differential equations of jump type are used in the theory of measurements continuous in time in quantum mechanics and have a concrete application in describing direct detection in quantum optics (counting of photons). In the paper the connections are explained among various types of stochastic equations: linear for Hilbert-space unnormalized vectors, non-linear for Hilbert space normalized vectors, linear for trace-class
operators, non-linear for density matrices. These equations allow to construct a posteriori states and probabilities for the counting process describing the direct detection. Relations with master equations and a priori states are also explained. Two concrete applications related to a
two-level atom are presented. |
|
