On the scarcity of contravariant left adjunctions

It is shown that any pair of contravariant mutually left adjoint functors between varieties of algebrasC andD factors through the retractions of these categories onto the complete lattices of epimorphs of their respective initial objects, and is thus fairly degenerate. However, some interesting contravariant left adjoint functors do exist between categories of finitely generated (or otherwise restricted) algebras.This work was done while the author was partly supported by NSF contract DMS 85-02330.Presented by F. E. J. Linton.     

Synthesis and reactivity of the monomeric late-transition-metal parent amido complex [Ir(Cp*)(PMe3)(Ph)(NH2)

The late-transition-metal parent amido compound [Ir(Cp*)(PMe3)(Ph)(NH2)] (2) has been synthesized by deprotonation of the corresponding ammine complex [Ir(Cp*)(PMe3)(Ph)(NH3)][OTf] (6) with KN(SiMe3)2. An X-ray structure determination has ascertained its monomeric nature. Proton-transfer studies indicate that 2 can successfully deprotonate p-nitrophenylacetonitrile, aniline, and phenol. Crystallographic analysis has revealed that the ion pair [Ir(Cp*)(PMe3)(Ph)(NH3)][OPh] (8) exists as a hydrogen-bonded dimer in the solid state. Reactions of 2 with isocyanates and carbodiimides lead to overall insertion of the heterocumulenes into the N--H bond of the Ir-bonded amido group, demonstrating the ability of 2 to act as an efficient nucleophile. Intriguing reactivity is observed when amide 2 reacts with CO or 2,6-dimethylphenyl isocyanide. eta4-Tetramethylfulvene complexes [Ir(eta4-C5Me4CH2)(PMe3)(Ph)(L)] (L=CO (15), CNC6H3-2,6-(CH3)2 (16)) are formed in solution through displacement of the amido group by the incoming ligand followed by deprotonation of a methyl group on the Cp* ring and liberation of ammonia. Conclusive evidence for the presence of the Ir-bonded eta4-tetramethylfulvene moiety in the solid state has been provided by an X-ray diffraction study of complex 16.     

Renormalization group analysis of a constrained Ising model

A Hamiltonian formulation is used to describe a constrained Ising system which has a non-gaussian tricritical point and renormalized Ising critical exponents. Renormalization group analysis reveals the fixed points which characterize this behavior.     

Rh(III)-catalyzed oxidative coupling of unactivated alkenes via C-H activation

Oxime directed aromatic C-H bond activation and oxidative coupling to alkenes is reported using a cationic Rh(III) catalyst. Significantly, the method can be used to oxidatively couple unactivated, aliphatic alkenes.     

Targeted energy transfers in vibro-impact oscillators for seismic mitigation

In the field of seismic protection of structures, it is crucial to be able to diminish ‘as much as possible’ and dissipate ‘as fast as possible’ the load induced by seismic (vibration-shock) energy imparted to a structure by an earthquake. In this context, the concept of passive nonlinear energy pumping appears to be natural for application to seismic mitigation. Hence, the overall problem discussed in this paper can be formulated as follows: Design a set of nonlinear energy sinks (NESs) that are locally attached to a main structure, with the purpose of passively absorbing a significant part of the applied seismic energy, locally confining it and then dissipating it in the smallest possible time. Alternatively, the overall goal will be to demonstrate that it is feasible to passively divert the applied seismic energy from the main structure (to be protected) to a set of preferential nonlinear substructures (the set of NESs), where this energy is locally dissipated at a time scale fast enough to be of practical use for seismic mitigation. It is the aim of this work to show that the concept of nonlinear energy pumping is feasible for seismic mitigation. We consider a two degree-of-freedom (DOF) primary linear system (the structure to be protected) and study seismic-induced vibration control through the use of Vibro-Impact NESs (VI NESs). Also, we account for the possibility of attaching to the primary structure additional alternative NES configurations possessing essential but smooth nonlinearities (e.g., with no discontinuities). We study the performance of the NESs through a set of evaluation criteria. The damped nonlinear transitions that occur during the operation of the VI NESs are then studied by superimposing wavelet spectra of the nonlinear responses to appropriately defined frequency – energy plots (FEPs) of branches of periodic orbits of underlying Conservative systems.     

Improved rigorous bounds on the effective elastic moduli of a composite material

A new method for deriving rigorous bounds on the effective elastic constants of a composite material is presented and used to derive a number of known as well as some new bounds. The new approach is based on a presentation of those constants as a sum of simple poles. The locations and strengths of the poles are treated as variational parameters, while different kinds of available information are translated into constraints on these parameters. Our new results include an extension of the range of validity of the Hashin-Shtrikman bounds to the case of composites made of isotropic materials but with an arbitrary microgeometry. We also use information on the effective elastic constants of one composite in order to obtain improved bounds on the effective elastic constants of another composite with the same or a similar microgeometry.     

Energy Transfers in a System of Two Coupled Oscillators with Essential Nonlinearity: 1:1 Resonance Manifold and Transient Bridging Orbits

The purpose of this study is to highlight and explain the vigorous energy transfers that may take place in a linear oscillator weakly coupled to an essentially nonlinear attachment, termed a nonlinear energy sink. Although these energy exchanges are encountered during the transient dynamics of the damped system, it is shown that the dynamics can be interpreted mainly in terms of the periodic orbits of the underlying Hamiltonian system. To this end, a frequency-energy plot gathering the periodic orbits of the system is constructed which demonstrates that, thanks to a 1:1 resonance capture, energy can be irreversibly and almost completely transferred from the linear oscillator to the nonlinear attachment. Furthermore, it is observed that this nonlinear energy pumping is triggered by the excitation of transient bridging orbits compatible with the nonlinear attachment being initially at rest, a common feature in most practical applications. A parametric study of the energy exchanges is also performed to understand the influence of the parameters of the nonlinear energy sink. Finally, the results of experimental measurements supporting the theoretical developments are discussed. This study was carried out while the author was a postdoctoral fellow at the National Technical University of Athens and at the University of Illinois at Urbana-Champaign.     

Seismic base isolation by nonlinear mode localization

Summary In this paper, the performance of a nonlinear base-isolation system, comprised of a nonlinearly sprung subfoundation tuned in a 1∶1 internal resonance to a flexible mode of the linear primary structure to be isolated, is examined. The application of nonlinear localization to seismic isolation distinguishes this study from other base-isolation studies in the literature. Under the condition of third-order smooth stiffness nonlinearity, it is shown that a localized nonlinear normal mode (NNM) is induced in the system, which confines energy to the subfoundation and away from the primary or main structure. This is followed by a numerical analysis wherein the smooth nonlinearity is replaced by clearance nonlinearity, and the system is excited by ground motions representing near-field seismic events. The performance of the nonlinear system is compared with that of the corresponding linear system through simulation, and the sensitivity of the isolation system to several design parameters is analyzed. These simulations confirm the existence of the localized NNM, and show that the introduction of simple clearance nonlinearity significantly reduces the seismic energy transmitted to the main structure, resulting in significant attenuation in the response. This work was supported in part by the National Science Foundation Grant CMS 00-00060. The authors are grateful for this support.