A note on the necessary conditions for the algebraic Riccati equation

We derive some useful and easily computable necessary conditionsfor the existence of a positive semi-definite solution to thealgebraic Ricatti equation (ARE). A motivating example is givento highlight the usefulness of the conditions for controllerand observer designs for nonlinear systems. Further, an upperbound on the trace of the solution to the ARE is also derived.     

Karhunen–Loeve representations of turbulent channel flows using the method of snapshots

For three‐dimensional flows with one inhomogeneous spatial coordinate and two periodic directions, the Karhunen–Loeve procedure is typically formulated as a spatial eigenvalue problem. This is normally referred to as the direct method (DM). Here we derive an equivalent formulation in which the eigenvalue problem is formulated in the temporal coordinate. It is shown that this so‐called method of snapshots (MOS) has some numerical advantages when compared to the DM. In particular, the MOS can be formulated purely as a matrix composed of scalars, thus avoiding the need to construct a matrix of matrices as in the DM. In addition, the MOS avoids the need for so‐called weight functions, which emerge in the DM as a result of the non‐uniform grid typically employed in the inhomogeneous direction. The avoidance of such weight functions, which may exhibit singular behaviour, guarantees satisfaction of the boundary conditions. The MOS is applied to data sets recently obtained from the direct simulation of turbulence in a channel in which viscoelasticity is imparted to the fluid using a Giesekus model. The analysis reveals a steep drop in the dimensionality of the turbulence as viscoelasticity is increased. This is consistent with the results that have been obtained with other viscoelastic models, thus revealing an essential generic feature of polymer‐induced drag reduced turbulent flows. Published in 2006 by John Wiley & Sons, Ltd.     

Electronic molecule-like spectrum of quantum wells in crossed fields

We show that an electron confined to a single finite parabolic quantum well in crossed electric and magnetic fields can behave as a double quantum well system. The magnetic field is parallel to the heterostructure layers and the electric field is perpendicular to those. For a suitable choice of both fields and quantum well width, the electron can be confined to a double quantum well effective potential that is very similar to the electronic potential model for diatomic molecules. The double quantum well spectrum is calculated using a numerical algorithm based on semiclassical methods. A physical interpretation of this quantum system is given based on the analogy to the electrons bound to diatomic molecules.     

On asymptotic approximation of a solution of a boundary-value problem for a nonlinear nonautonomous equation

On the basis of periodic Ateb functions, in the resonance and nonresonance cases, we construct the asymptotic approximation of one-frequency solutions of a boundary-value problem for a nonlinear nonautonomous equation.     

Vibrational control of crystal growth from liquid phase

Modeling and numerical simulations of the convective flows induced by the vibration of the monocrystal during crystal growth have been performed for two configurations simulating the Cz and FZ methods. This permitted to emphasize the role of different vibrational mechanisms in the formation of the average flows. It is shown that an appropriate combination of these mechanisms can be used to counteract the usual convective flows (buoyancy- and/or thermocapillary-driven) inherent to crystal growth processes from the liquid phase. While vibrational convection is rather complex due to these identified mechanisms, the new modeling used in the present paper opens up very promising perspectives to efficiently control heat and mass transfer during real industrial applications of crystal growth from the liquid phase.     

Kinetics of benzonitrile nitration with mixed acid under homogeneous conditions

Chemical kinetics of benzonitrile nitration with mixed acid is investigated in the temperature range 283–299 K. Pseudo-first-order rate constants are evaluated by means of rate experiments on homogeneous reacting mixtures having large stoichiometric excesses of nitric acid. The second-order kinetic constants for nitronium ion attack to the aromatic substrate are derived on the basis of the assessed nitration mechanism. An activation energy of 604 ± 37 kJ mol^?1 is calculated for this reaction step. © 1993 John Wiley & Sons, Inc.     

AN ALTERNATIVE SPECIFICATION FOR MODELING GROUNDWATER DYNAMICS

This research extends previous work with dynamic models to manage groundwater quality by using the consumptive nitrate use rate instead of the nitrate application rate. The analysis indicates that misspecification results in overestimation of economic benefits, and supra-optimum nitrogen fertilizer application rates and groundwater nitrate stocks at a steady state.