Exact traveling- wave solution for model geophysical systems

Exact traveling-wave solutions of time-dependent nonlinear inhomogeneous PDEs, describing several model systems in geophysical fluid dynamics, are found. The reduced nonlinear ODEs are treated as systems of linear algebraic equations in the derivatives. A variety of solutions are found, depending on the rank of the algebraic systems. The geophysical systems include acoustic gravity waves, inertial waves, and Rossby waves. The solutions describe waves which are, in general, either periodic or monoclinic. The present approach is compared with the earlier one due to Grundland (1974) for finding exact solutions of inhomogeneous systems of nonlinear PDEs.

Diruthenium(III) compounds, Ru2O(O2CAr)2(MeCN)4(PPh3)2(ClO4)2.cntdot.H2O and Ru2O(O2CAr)4(PPh3)2, with an (Ru2(.mu.-O)(.mu.-O2CAr)22+) core as model systems for the diiron centers in hemerythrin

Diruthenium(II1) compounds, Ru20(02CAr)2(MeCN)4(PPh3)2(C104)(z1~) Hazn0d R U ~ O ( O ~ C A ~ ) ~(2() P(PA~r ~= )P~h,C6H4-p-OMe), were prepared by reacting R U ~ C I ( O ~ CaAnd~ P)P~h 3 in MeCN and characterized by analytical and spectral data. The molecular structures of 1 with Ar = Ph and of 2 with Ar = C&p-OMe were determined by X-ray crystallography. Crystal data for Ru~~(~~CP~)~(M~CN),(PP~(~la)):~ m(oCnIoc~lin,ic), n~/~cH, ~a O= 27.722 (3) A, b = 10.793 (2) A, c = 23.445 ( 2 )A , fi = 124.18 (l)', V = 5803 A3, and 2 = 4. Cr stal data for Ru~O(O~CC~H~-~-O(M2b~): )o~rth(orPhoPm~bi~c, )Pn~n a, a = 22.767 (5) A, b = 22.084 (7) A, c = 12.904 (3) 1, V = 6488 AS; and 2 = 4. Both 1 and 2 have an (Ruz0(02CAr)z2t1 core that is analogous to the diiron core present in the oxidized form of the nonheme respiratory protein hemerythrin. The Ru-Ru distances of 3.237 (1) and 3.199 ( I ) A observed in 1 and 2, respectively, are similar to the M-M distances known in other model systems. The essentially diamagnetic nature of 1 and 2 is due to the presence of two strongly interacting t22 Ru"' centers. The intense colors of 1 (blue) and 2 (purple) are due to the charge-transfer transition involving an ( R ~ ~ ( f i - 0m)o~ie~ty.) The presence of labile MeCN and carboxylato ancillary ligands in I and 2, respectively, makes these systems reactive toward amine and heterocyclic bases.

Model of resistances in systems of Tomonaga-Luttinger liquid wires

In a recent paper, we combined the technique of bosonization with the concept of a Rayleigh dissipation function to develop a model for resistances in one-dimensional systems of interacting spinless electrons Europhys. Lett. 93, 57007 (2011)]. We also studied the conductance of a system of three wires by using a current splitting matrix M at the junction. In this paper, we extend our earlier work in several ways. The power dissipated in a three-wire system is calculated as a function of M and the voltages applied in the leads. By combining two junctions of three wires, we examine a system consisting of two parallel resistances. We study the conductance of this system as a function of the M matrices and the two resistances; we find that the total resistance is generally quite different from what one expects for a classical system of parallel resistances. We do a sum over paths to compute the conductance of this system when one of the two resistances is taken to be infinitely large. We study the conductance of a three-wire system of interacting spin-1/2 electrons, and show that the charge and spin conductances can generally be different from each other. Finally, we consider a system of two wires that are coupled by a dissipation function, and we show that this leads to a current in one wire when a voltage bias is applied across the other wire.

Convergence problems in a class of model reference adaptive control systems

A class of model reference adaptive control system which make use of an augmented error signal has been introduced by Monopoli. Convergence problems in this attractive class of systems have been investigated in this paper using concepts from hyperstability theory. It is shown that the condition on the linear part of the system has to be stronger than the one given earlier. A boundedness condition on the input to the linear part of the system has been taken into account in the analysis - this condition appears to have been missed in the previous applications of hyperstability theory. Sufficient conditions for the convergence of the adaptive gain to the desired value are also given.

Time variant reliability model updating in instrumented dynamical systems based on Girsanov's transformation

The problem of updating the reliability of instrumented structures based on measured response under random dynamic loading is considered. A solution strategy within the framework of Monte Carlo simulation based dynamic state estimation method and Girsanov's transformation for variance reduction is developed. For linear Gaussian state space models, the solution is developed based on continuous version of the Kalman filter, while, for non-linear and (or) non-Gaussian state space models, bootstrap particle filters are adopted. The controls to implement the Girsanov transformation are developed by solving a constrained non-linear optimization problem. Numerical illustrations include studies on a multi degree of freedom linear system and non-linear systems with geometric and (or) hereditary non-linearities and non-stationary random excitations.

State estimation in power systems using linear model infinity norm-based trust region approach

State estimation is one of the most important functions in an energy control centre. An computationally efficient state estimator which is free from numerical instability/ill-conditioning is essential for security assessment of electric power grid. Whereas approaches to successfully overcome the numerical ill-conditioning issues have been proposed, an efficient algorithm for addressing the convergence issues in the presence of topological errors is yet to be evolved. Trust region (TR) methods have been successfully employed to overcome the divergence problem to certain extent. In this study, case studies are presented where the conventional algorithms including the existing TR methods would fail to converge. A linearised model-based TR method for successfully overcoming the convergence issues is proposed. On the computational front, unlike the existing TR methods for state estimation which employ quadratic models, the proposed linear model-based estimator is computationally efficient because the model minimiser can be computed in a single step. The model minimiser at each step is computed by minimising the linearised model in the presence of TR and measurement mismatch constraints. The infinity norm is used to define the geometry of the TR. Measurement mismatch constraints are employed to improve the accuracy. The proposed algorithm is compared with the quadratic model-based TR algorithm with case studies on the IEEE 30-bus system, 205-bus and 514-bus equivalent systems of part of Indian grid.

Time variant reliability model updating in instrumented dynamical systems based on Girsanov’s transformation

The problem of updating the reliability of instrumented structures based on measured response under random dynamic loading is considered. A solution strategy within the framework of Monte Carlo simulation based dynamic state estimation method and Girsanov’s transformation for variance reduction is developed. For linear Gaussian state space models, the solution is developed based on continuous version of the Kalman filter, while, for non-linear and (or) non-Gaussian state space models, bootstrap particle filters are adopted. The controls to implement the Girsanov transformation are developed by solving a constrained non-linear optimization problem. Numerical illustrations include studies on a multi degree of freedom linear system and non-linear systems with geometric and (or) hereditary non-linearities and non-stationary random excitations.