Concentration of low energy extremals

Concentration of low energy extremals: Identification of concentration points

Energy assessment of enhanced fixed low concentration photovoltaic systems

In order to exploit as much as possible the surfaces apt for installation of photovoltaic (PV) systems and also to keep the unit energy cost low (without increasing meaningfully capital and operation/maintenance costs), fixed low concentration systems (LCPVs) can be adopted, such systems are normally based on flat mirrors. LCPVs can be either fixed or tracked, but in this paper the fixed soluti...

Optimality of Broken Extremals

In this paper we analyse the optimality of broken Pontryagin extremal for an n -dimensional affine control system with a control parameter, taking values in a k dimensional closed ball. We prove the optimality of broken normal extremals when n = 3 and the controllable vector fields form a contact distribution, and when the Lie algebra of the controllable fields is locally orthogonal to the sing...

Nonregular Abnormal Extremals

We study existence and rigidity (W1-isolatedness) of nonregular abnormal extremals of completely nonholonomic 2-distribution (nonregularity means that such extremals do not satisfy the strong generalized Legendre-Clebsch condition). Introducing the notion of diagonal form of the second variation, we generalize some results of A. Agrachev and A. Sarychev about rigidity of regular abnormal extrem...

Extremals of Determinants of Laplacians

The modern quantum geometry of strings is concerned to a large extent with the set of all surfaces, with varying metrics on those surfaces, and with determinants of associated Laplacians. Our aim in this paper is to study this determinant as a function of the metric on a given surface and in particular its extreme values when the metric is suitably restricted. This kind of problem has actually ...