Nonlinear stability of Euler flows in two-dimensional periodic domains

The non-quadratic conservation laws of the two-dimensional Euler equations are used to show that the gravest modes in a doubly-periodic domain with aspect ratio L = 1 are stable up to translations (or structurally stable) for finite-amplitude disturbances. This extends a previous result based on conservation of energy and enstrophy alone. When L 1, a saturation bound is established for the mode with wavenumber |k| = L −1 (the next-gravest mode), which is linearly unstable. The method is applied to prove nonlinear structural stability of planetary wave two on a rotating sphere.

Mono- and binuclear bipyridyl derivatives of the Mo(eta(3)-C3H5)(CO)(2) fragment: structural studies and fluxionality in solution

New mono- and binuclear complexes of the Mo(eta(3)-C3H5)(CO)(2) fragment, containing bipyridyl ligands (2,2'-bpy, 4,4'-Me-2-2,2'-bpy) as chelates, and mono- (4-CNpy, 4-Mepy, NCMe, Br) or bidentate nitrogen ligands (4,4'-bpy, bipyridylethylene, pyrazine) as terminal or bridging ligands, respectively, were prepared. The binuclear complex [{Mo(eta(3)-C3H5)(CO)(2)(2,2'-bpy)}(2)(mu-4,4'-bpy)][PF6](2) (2) was shown by X-ray diffraction to assemble in the crystal forming large channels with a rectangular section. A longer bridge, such as bipyridylethylene, led to a different structure (3). 4-CNpy behaved as monodentate ligand (4), coordinating through the pyridine nitrogen as a terminal ligand. NMR spectroscopy studies showed that the complexes exhibited a fluxional behavior in solution, the endo and exo forms of the more symmetrical equatorial isomers being usually present and interconverting in solution. The solid state structures of the complexes revealed a preference for the more symmetrical equatorial isomer, with the two chelate ligands in trans positions in the binuclear species. The rings tended to become parallel in the organized crystal. (C) 2003 Elsevier B.V. All rights reserved.

Robust nonlinear model identification methods using forward regression

In this correspondence new robust nonlinear model construction algorithms for a large class of linear-in-the-parameters models are introduced to enhance model robustness via combined parameter regularization and new robust structural selective criteria. In parallel to parameter regularization, we use two classes of robust model selection criteria based on either experimental design criteria that optimizes model adequacy, or the predicted residual sums of squares (PRESS) statistic that optimizes model generalization capability, respectively. Three robust identification algorithms are introduced, i.e., combined A- and D-optimality with regularized orthogonal least squares algorithm, respectively; and combined PRESS statistic with regularized orthogonal least squares algorithm. A common characteristic of these algorithms is that the inherent computation efficiency associated with the orthogonalization scheme in orthogonal least squares or regularized orthogonal least squares has been extended such that the new algorithms are computationally efficient. Numerical examples are included to demonstrate effectiveness of the algorithms.

Synthesis, structural characterization and electrochemical activity of oxidovanadium(IV/V) complexes of a diprotic ONS chelating ligand

The present work reports the chemistry of a few oxidovanadium(IV) and (V) complexes of the ONS chelating ligand S-benzyl-beta-N-(2-hydroxyphenylethylidine) dithiocarbazate (H2L). Major objective of this work is to arrive at some general conclusions about the influence of binding environment generated by the replacement of an O-donor center by a S-donor point in a ligand (of a similar arrangement of the other O- and N-donor points) on the redox behavior and on the structural features of comparable [VO(OEt)(ONS)] and [VO(OEt)(ONO)] complexes. Synthesis, characterization by various physicochemical techniques (UV-Vis, IR, EPR and elemental analysis), exploration of electrochemical activity of the oxidovanadium(V) complex [(VO)-O-V(OEt) L] (1), the mixed ligand complex [(VO)-O-V(N-O)L] (3) (where N-O is the mono anion of 8-hydroxyquinoline) and a binuclear complex [(VO)-O-V(OEt)L](2)(mu-4,4'-bipy) (2) are reported. Similar studies on of mixed ligand oxidovanadium(IV) complexes of the formula [(VO)-O-V(N-N)L] (4,5) (where N-N = 2,2'-bipy and o-phen) are also presented here. The [(VO)-O-V(OEt)L] complex is pentacoordinated and distorted square pyramidal, while the [V-IV(N-N)L] complexes are hexacoordinated and octahedral. Structural features of the complex 1 were compared with the corresponding aspects of the previously reported analogous complex [(VO)-O-V(OEt)(ONO)] (1').

Classifying general nonlinear force laws in cell-based models via the continuum limit

though discrete cell-based frameworks are now commonly used to simulate a whole range of biological phenomena, it is typically not obvious how the numerous different types of model are related to one another, nor which one is most appropriate in a given context. Here we demonstrate how individual cell movement on the discrete scale modeled using nonlinear force laws can be described by nonlinear diffusion coefficients on the continuum scale. A general relationship between nonlinear force laws and their respective diffusion coefficients is derived in one spatial dimension and, subsequently, a range of particular examples is considered. For each case excellent agreement is observed between numerical solutions of the discrete and corresponding continuum models. Three case studies are considered in which we demonstrate how the derived nonlinear diffusion coefficients can be used to (a) relate different discrete models of cell behavior; (b) derive discrete, intercell force laws from previously posed diffusion coefficients, and (c) describe aggregative behavior in discrete simulations.

The study of chiral adsorption systems using synchrotron- based structural and spectroscopic techniques: stereospecific adsorption of serine on Au-modified chiral Cu{531} surfaces

We apply modern synchrotron-based structural techniques to the study of serine adsorbed on the pure andAumodified intrinsically chiral Cu{531} surface. XPS and NEXAFS data in combination with DFT show that on the pure surface both enantiomers adsorb in l4 geometries (with de-protonated b-OH groups) at low coverage and in l3 geometries at saturation coverage. Significantly larger enantiomeric differences are seen for the l4 geometries, which involve substrate bonds of three side groups of the chiral center, i.e. a three-point interaction. The l3 adsorption geometry, where only the carboxylate and amino groups form substrate bonds, leads to smaller but still significant enantiomeric differences, both in geometry and the decomposition behavior. When Cu{531} is modified by the deposition of 1 and 2ML Au the orientations of serine at saturation coverage are significantly different from those on the clean surface. In all cases, however, a l3 bond coordination is found at saturation involving different numbers of Au atoms, which leads to relatively small enantiomeric differences.

Evidence of dispersion relations for the nonlinear response of the Lorenz 63 system

Along the lines of the nonlinear response theory developed by Ruelle, in a previous paper we have proved under rather general conditions that Kramers-Kronig dispersion relations and sum rules apply for a class of susceptibilities describing at any order of perturbation the response of Axiom A non equilibrium steady state systems to weak monochromatic forcings. We present here the first evidence of the validity of these integral relations for the linear and the second harmonic response for the perturbed Lorenz 63 system, by showing that numerical simulations agree up to high degree of accuracy with the theoretical predictions. Some new theoretical results, showing how to derive asymptotic behaviors and how to obtain recursively harmonic generation susceptibilities for general observables, are also presented. Our findings confirm the conceptual validity of the nonlinear response theory, suggest that the theory can be extended for more general non equilibrium steady state systems, and shed new light on the applicability of very general tools, based only upon the principle of causality, for diagnosing the behavior of perturbed chaotic systems and reconstructing their output signals, in situations where the fluctuation-dissipation relation is not of great help.

Exact design manifold control of a class of nonlinear singularly perturbed systems

The integral manifold approach captures from a geometric point of view the intrinsic two-time-scale behavior of singularly perturbed systems. An important class of nonlinear singularly perturbed systems considered in this note are fast actuator-type systems. For a class of fast actuator-type systems, which includes many physical systems, an explicit corrected composite control, the sum of a slow control and a fast control, is derived. This corrected control will steer the system exactly to a required design manifold.

Exact design manifold control of a class of nonlinear singularly perturbed systems

The integral manifold approach captures from a geometric point of view the intrinsic two-time-scale behavior of singularly perturbed systems. An important class of nonlinear singularly perturbed systems considered in this note are fast actuator-type systems. For a class of fast actuator-type systems, which includes many physical systems, an explicit corrected composite control, the sum of a slow control and a fast control, is derived. This corrected control will steer the system exactly to a required design manifold.

Bifurcation Analysis of Eigenstructure Assignment Control in a Simple Nonlinear Aircraft Model

Aircraft systems are highly nonlinear and time varying. High-performance aircraft at high angles of incidence experience undesired coupling of the lateral and longitudinal variables, resulting in departure from normal controlled � ight. The construction of a robust closed-loop control that extends the stable and decoupled � ight envelope as far as possible is pursued. For the study of these systems, nonlinear analysis methods are needed. Previously, bifurcation techniques have been used mainly to analyze open-loop nonlinear aircraft models and to investigate control effects on dynamic behavior. Linear feedback control designs constructed by eigenstructure assignment methods at a � xed � ight condition are investigated for a simple nonlinear aircraft model. Bifurcation analysis, in conjunction with linear control design methods, is shown to aid control law design for the nonlinear system.

Closed loop design for a simple nonlinear aircraft model using eigenstructure assignment

Aircraft systems are highly nonlinear and time varying. High-performance aircraft at high angles of incidence experience undesired coupling of the lateral and longitudinal variables, resulting in departure from normal controlled flight. The aim of this work is to construct a robust closed-loop control that optimally extends the stable and decoupled flight envelope. For the study of these systems nonlinear analysis methods are needed. Previously, bifurcation techniques have been used mainly to analyze open-loop nonlinear aircraft models and investigate control effects on dynamic behavior. In this work linear feedback control designs calculated by eigenstructure assignment methods are investigated for a simple aircraft model at a fixed flight condition. Bifurcation analysis in conjunction with linear control design methods is shown to aid control law design for the nonlinear system.

Steric effects on uranyl complexation: synthetic, structural, and theoretical studies of carbamoyl pyrazole compounds of the uranyl(VI) ion

New bifunctional pyrazole based ligands of the type [C3HR2N2CONR'] (where R = H or CH3; R' = CH3, C2H5, or (C3H7)-C-i) were prepared and characterized. The coordination chemistry of these ligands with uranyl nitrate and uranyl bis(dibenzoyl methanate) was studied with infrared (IR), H-1 NMR, electrospray-mass spectrometry (ES-MS), elemental analysis, and single crystal X-ray diffraction methods. The structure of compound [UO2(NO3)(2)(C3H3N2CON{C2H5}(2))] (2) shows that the uranium(VI) ion is surrounded by one nitrogen atom and seven oxygen atoms in a hexagonal bipyramidal geometry with the ligand acting as a bidentate chelating ligand and bonds through both the carbamoyl oxygen and pyrazolyl nitrogen atoms. In the structure of [UO2(NO3)(2)(H2O)(2)(C5H7N2CON {C2H5}(2))(2)], (5) the pyrazole figand acts as a second sphere ligand and hydrogen bonds to the water molecules through carbamoyl oxygen and pyrazolyl nitrogen atoms. The structure of [UO2(DBM)(2)C3H3N2CON{C2H5}(2)] (8) (where DBM = C6H5COCHCOC6H5) shows that the pyrazole ligand acts as a monodentate ligand and bonds through the carbamoyl oxygen to the uranyl group. The ES-MS spectra of 2 and 8 show that the ligand is similarly bonded to the metal ion in solution. Ab initio quantum chemical studies show that the steric effect plays the key role in complexation behavior.