Preferential attachment in growing spatial networks

We obtain the degree distribution for a class of growing network models on flat and curved spaces. These models evolve by preferential attachment weighted by a function of the distance between nodes. The degree distribution of these models is similar to the one of the fitness model of Bianconi and Barabasi, with a fitness distribution dependent on the metric and the density of nodes. We show that curvature singularities in these spaces can give rise to asymptotic Bose-Einstein condensation, but transient condensation can be observed also in smooth hyperbolic spaces with strong curvature. We provide numerical results for spaces of constant curvature (sphere, flat and hyperbolic space) and we discuss the conditions for the breakdown of this approach and the critical points of the transition to distance-dominated attachment. Finally we discuss the distribution of link lengths.Comment: 9 pages, 12 figures, revtex, final versio

Valuation of R&D Sequential Exchange Options using Monte Carlo approach

This article describes a methodology for evaluating R&D investment projects using Monte Carlomethods. R&D projects generally involves multiple phases with or without overlapping. R&D investments are made often in a phased manner, with the commencement of subsequent phase being dependent on the successful completion of the preceding phase, it is known as sequential investment. Moreover, each stage creates an opportunity (option) for subsequent investment. Therefore, R&D projects can be considered as ‘Compound Options' in which investments present uncertainty both in the gross project value and in costs. It is possible to use exchange options to value the R&D investment opportunities. In this paper, we propose to value the European and American Real Compound Exchange options through Monte Carlo simulation. We also provide a set of numerical experiments to provide evidence for the accuracy of the proposed methodology.Pseudo Compound American Exchange option; R&D;Monte Carlo Methods.

An example of active circulation control of the unsteady separated flow past a semi-infinite plate

Active circulation control of the two-dimensional unsteady separated flow past a semiinfinite plate with transverse motion is considered. The rolling-up of the separated shear layer is modelled by a point vortex whose time-dependent circulation is predicted by an unsteady Kutta condition. A suitable vortex shedding mechanism introduced. A control strategy able to maintain constant circulation when a vortex is present is derived. An exact solution for the nonlinear controller is then obtained. Dynamical systems analysis is used to explore the performance of the controlled system. The control strategy is applied to a class of flows and the results are discussed. A procedure to determine the position and the circulation of the vortex, knowing the velocity signature on the plate, is derived. Finally, a physical explanation of the control mechanism is presented

Nonlinear feedback control of the wake past a plate with a suction point on the downstream wall

Active circulation control of the two-dimensional unsteady separated how past a plate with a suction point on the downstream wall is considered. The rolling-up of the separated shear layer is modelled by a pair of point vortices whose time-dependent circulation is predicted by an unsteady Kutta condition. A nonlinear controller able to confine the wake to a single vortex pair of constant circulation is derived in closed form for any free-stream condition. Dynamical system analysis is used to explore the performance of the controlled system. Finally, the control strategy is applied to three different classes of unsteady flows and the results are discussed