Influence of Equilibration Time in Solution on the Inclusion/Exclusion Topology Ratio of Host–Guest Complexes Probed by Ion Mobility and Collision‐Induced Dissociation

Host–guest complexes are formed by the creation of multiple noncovalent bonds between a large molecule (the host) and smaller molecule(s) or ion(s) (the guest(s)). Ion‐mobility separation coupled with mass spectrometry nowadays represents an ideal tool to assess whether the host–guest complexes, when transferred to the gas phase upon electrospray ionization, possess an exclusion or inclusion nature. Nevertheless, the influence of the solution conditions on the nature of the observed gas‐phase ions is often not considered. In the specific case of inclusion complexes, kinetic considerations must be taken into account beside thermodynamics; the guest ingression within the host cavity can be characterized by slow kinetics, which makes the complexation reaction kinetically driven on the timescale of the experiment. This is particularly the case for the cucurbituril family of macrocyclic host molecules. Herein, we selected para‐phenylenediamine and cucurbit[6]uril as a model system to demonstrate, by means of ion mobility and collision‐induced dissociation measurements, that the inclusion/exclusion topology ratio varies as a function of the equilibration time in solution prior to the electrospray process.     

The EU regulation on cross-border trade of electricity: A two-stage equilibrium model

The regulation on cross-border exchanges of electricity in the European Union is meant to enhance the trade of electricity between Member States, by facilitating access to the network and improving the management of congestion at the interconnections. This paper presents a computational model that embeds these two features. The problem is cast in the form of a two-stage equilibrium between regional Regulators. In the first stage, they decide on the allocation of their regional network costs between generators and customers. Either they maximise their regional welfare non-cooperatively (Nash equilibrium), or they centralise the decision as a super-regulator (leading to a cooperative equilibrium). In the second-stage equilibrium, the consequences of first-stage’s decisions are assessed by modelling the energy market as the result of imperfect competition equilibrium on competitive market, coupled with regulated pricing on the domestic less competitive markets. The “rules” that come out of the first-stage game largely influence the final equilibrium. We illustrate this on an extensive numerical example, showing that the model behaves properly and identifying policy issues worth of further investigations.     

Theory and practice of long-period gratings: when a loss becomes a gain

Losses of cladding modes are part of the mechanism of operation of a long-period grating (LPG) when it is used as an optical filter. We present a LPG computer simulation that accounts for these losses. On the basis of this simulation, we show that losses result in qualitatively different LPG spectral behavior. There is an optimal loss value that provides sidelobe-free, 100% power transfer from the core to the cladding mode for a uniform LPG. We obtained a simple equation that relates this optimum lose value to the LPG length and the cross-coupling coefficient. Based on the results, we propose new approaches to LPG design in a fiber as well as in waveguide platforms for fiber-optic communication and sensor applications. A design of a LPG reconfigurable filter is suggested.     

Fibre mode expansion for 2-D waveguide calculations

A numerical method is introduced which is devised to calculate the lower-order modes of optical waveguides with two-dimensional transverse index profiles embedded in a homogeneous cladding medium. We propose a method based on a series expansion using guided modes of an optical fibre. To test the method, it is applied to a three-layer optical-fibre and the results are compared with the exact analytical solutions. The error in the calculation of the modal effective indices is found to be less than 10−6. This method allows the modelling of symmetric 2 × 2 completely fused fibre couplers. Effective indices and polarization corrections are compared with results obtained by the field correction method. The adiabaticity criterion is calculated for these couplers. This revised version was published online in November 2006 with corrections to the Cover Date.