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.     

A non-MRA C^r Frame Wavelet with Rapid Decay

A generalized filter construction is used to build an example of a non-MRA normalized tight frame wavelet for dilation by 2 in . This example has the same multiplicity function as the Journé wavelet, yet has a Fourier transform and can be made to be for any fixed postive integer . L. Baggett and P. Jorgensen were supported by a US–NSF Focused Research Group (FRG) grant.     

Vinylferrocene homopolymer and copolymers: an electrochemical comparison.

Poly(vinylferrocene) (pVFc) homopolymer was synthesized by free radical polymerization, along with a series of pVFc-based copolymers containing either styrene, vinylanthracene or methylmethacrylate. This report details the electrochemical experiments conducted to examine the stability of the various pVFc based polymers, which is shown to be critically dependent on the extent of copolymerization. A trend was found that when the concentration of co-monomer was decreased, electrochemical stability was enhanced. Furthermore incorporation of a second monomer into the polymer chain produced a profound effect on the scan rate behaviour of the vinylferrocene moiety. As the concentration of co-monomer was decreased, the behaviour tended towards that of a diffusion controlled process. These results are of vital significance for the development of pVFc-based electrochemical sensors.     

Poly(methyl methacrylate) copolymers containing pendant carbazole and oxadiazole moieties for applications in single‐layer organic light emitting devices

Methyl methacrylate derived monomers functionalized with pendant carbazole and oxadiazole moieties were synthesized and could be copolymerized to form a random copolymer. The glass transition temperature of the copolymers could be predicted with a Fox equation and ranged from 140 to 191 °C. The photoluminescent characteristics of the copolymers, both in solution and in solid films, exhibited emission that was a combination of sharp and broad peaks, suggestive of monomeric and chromophore aggregation emission. These trends were also apparent in the electroluminescent response of the copolymers, where the appearance of an electromer emission was evident and was tentatively assigned to the carbazole moieties. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 7882–7897, 2008     

A Special Topics Course in Perturbation Methods

A special topics course dealing with perturbation methods in applied mathematics which was recently taught at Stevens Institute of Technology is described. Since the course enrolment was comprised of undergraduate and graduate mathematics students as well as graduate students in engineering, an unusual course philosophy had to be developed and implemented. The approach taken to achieve this in both teaching techniques and selection of subject matter is discussed in detail. Finally, conclusions are drawn from the students’ and the instructor's experiences with the course which hopefully will be of value to those considering offering special topics courses in the future.     

Multi-criteria logistics modeling for military humanitarian assistance and disaster relief aerial delivery operations

Given that it is not always feasible to reach an affected area via land or sea within the first week following a natural disaster, aerial delivery provides the primary means to rapidly supply the affected population. Further, it is often the case that high density delivery of humanitarian aid supplies are taken over by non-friendly groups within the affected population. By using direct airdrop systems to deliver large quantities of individually wrapped food and water items, dispersion among the affected disaster relief population will occur more quickly. In this paper, we proffer a multiple criteria decision analysis (MCDA) framework to optimize the military humanitarian assistance/disaster relief (HA/DR) aerial delivery supply chain network. The model uses stochastic, mixed-integer, weighted goal programming to optimize network design, logistics costs, staging locations, procurement amounts, and inventory levels. The MCDA framework enables decision-makers to explore the trade-offs between military HA/DR aerial delivery supply chain efficiency and responsiveness, while optimizing across a wide range of real-world, probabilistic scenarios to account for the inherent uncertainty in the location of global humanitarian disasters as well as the amount of demand to be met.