Passive control of aeroelastic instability in a long span bridge model prone to coupled flutter using targeted energy transfer

In this paper we study a problem of passive nonlinear targeted energy transfer between a two degrees of freedom long span bridge model prone to coupled flutter and a single degree of freedom nonlinear energy sink (NES). This study is mainly analytical and use complexification methods, multiple scales expansions and exploits also the concept of limiting phase trajectories (LPTs). The system is studied under 1:1:1 nonlinear resonance involved in targeted energy transfer mechanisms. Several behaviors that suppress aeroelastic instability are identified. We show that analytical calculations permit to design a NES able to efficiently control the aeroelastic instability of the bridge. Numerical simulations are performed and good agreement with analytical predictions is observed. It results that the concept of limiting phase trajectories (LPT) allows formulating adequately the problem of intensive energy transfer from a bridge to a nonlinear energy sink.     

Nonstationary energy localization vs conventional stationary localization in weakly coupled nonlinear oscillators

In this paper we study the effect of nonstationary energy localization in a nonlinear conservative resonant system of two weakly coupled oscillators. This effect is alternative to the well-known stationary energy localization associated with the existence of localized normal modes and resulting from a local topological transformation of the phase portraits of the system. In this work we show that nonstationary energy localization results from a global transformation of the phase portrait. A key to solving the problem is the introduction of the concept of limiting phase trajectories (LPTs) corresponding to maximum possible energy exchange between the oscillators. We present two scenarios of nonstationary energy localization under the condition of 1:1 resonance. It is demonstrated that the conditions of nonstationary localization determine the conditions of efficient targeted energy transfer in a generating dynamical system. A possible extension to multi-particle systems is briefly discussed.     

Carbon Nanotubes in Arrays: Competition of van-der-Waals and Elastic Forces

Doklady Physics - The van-der-Waals interaction between carbon nanotubes leads to the formation of agglomerates of bundles and strands. In such a self-assemblage, identical nanotubes are assembled...     

The soliton mechanism of phase separation of polydisperse multiblock copolymers

The equations of the thermodynamics of compressible polydisperse multiblock copolymers have been analytically and numerically studied. The possible density distributions of copolymer units over a wide temperature range including the cloud point and the spinodal temperature have been determined. Along with periodic structures, spatially localized soliton-type distributions have been identified in order to estimate the energy barrier that must be overcome for the occurrence of the initial stage of the phase transition.     

Energy transfer in weakly coupled nonlinear oscillator chains: Transition from a wandering breather to nonlinear self-trapping

We present analytical and numerical studies of phase-coherent dynamics of intrinsically localized excitations (breathers) in a system of two weakly coupled nonlinear oscillator chains. We show that there are two qualitatively different dynamical regimes of the coupled breathers, either immovable or slowly moving: the periodic wandering of the low-amplitude breather between the chains, and the one-chain-localization of the high-amplitude breather. These two modes of coupled breathers can be mapped exactly onto two solutions of a pendulum equation, detached by a separatrix mode. We also show that these two regimes of the coupled breathers are similar, and are described by a similar pair of equations, to the two regimes in the nonlinear tunneling dynamics of two weakly coupled Bose-Einstein condensates. On the basis of this analogy, we predict a new tunneling mode of two weakly coupled Bose-Einstein condensates in which their relative phase oscillates around π/2 modulo π.     

Dynamics of linear discrete systems connected to local, essentially non-linear attachments

The dynamics of a linear periodic substructure, weakly coupled to an essentially non-linear attachment are studied. The essential (non-linearizable) non-linearity of the attachment enables it to resonate with any of the linearized modes of the subtructure leading to energy pumping phenomena, e.g., passive, one-way, irreversible transfer of energy from the substructure to the attachment. As a specific application the dynamics of a finite linear chain of coupled oscillators with a non-linear end attachment is examined. In the absence of damping, it is found that the dynamical effect of the non-linear attachment is predominant in neighborhoods of internal resonances between the attachment and the chain. When damping exists energy pumping phenomena are realized in the system. It is shown that energy pumping strongly depends on the topological structure of the non-linear normal modes (NNMs) of the underlying undamped system. This is due to the fact that energy pumping is caused by the excitation of certain damped invariant NNM manifolds that are analytic continuations for weak damping of NNMs of the underlying undamped system. The bifurcations of the NNMs of the undamped system help explain resonance capture cascades in the damped system. This is a series of energy pumping phenomena occurring at different frequencies, with sudden lower frequency transitions between sequential events. The observed multi-frequency energy pumping cascades are particularly interesting from a practical point of view, since they indicate that non-linear attachments can be designed to resonate and extract energy from an a priori specified set of modes of a linear structure, in compatibility with the design objectives.     

Direct Antifungal Effect of Femtosecond Laser on Trichophyton rubrum Onychomycosis

Onychomycosis is caused by dermatophyte infection of the nail. Though laser energy has been shown to eliminate dermatophytes in vitro, direct laser elimination of onychomycosis is not successful due to difficulties in selectively delivering laser energy to the deeper levels of the nail plate without collateral damage. Femtosecond (fsec) infrared titanium sapphire lasers circumvent this problem by the nonlinear interactions of these lasers with biological media. This quality, combined with the deeply penetrating nature of the near-infrared radiation, allows elimination of deeply seeded nail dermatopytes without associated collateral damage. Nail cuttings obtained from patients with onychomycosis caused by Trichophyton rubrum underwent fsec laser irradiation using increasing laser intensities with the focus scanned throughout the whole thickness of the nail specimen. The efficacy of the laser treatment was evaluated by subculture. Scanning electron microscopy was used to determine fsec laser-induced collateral damage. We found that a fsec laser fluence of 7 × 10³¹ photons m⁻² s⁻¹ or above successfully inhibited the growth of the fungus in all samples examined, whereas laser intensities above 1.7 × 10³² photons m⁻² s⁻¹ affected the structure of the nail plate. Our findings suggest that T. rubrum-mediated onychomycosis may be treated by fsec laser technology.     

Diffusion of topological solitons and dielectric αc relaxation in a polymeric crystal

A molecular dynamics simulation was performed to estimate the effective mass and the diffusion and friction coefficients of point defects in macromolecular chains of crystalline polyethylene. The results were compared with theoretical mass and kinetic coefficient predictions for topological solitons, with which these defects were identified. The results are used to discuss the soliton model of dielectric α_c relaxation in weakly oxidized polyethylene.     

Transversal Dynamics of One-Dimensional Chain on Nonlinear Asymmetric Substrate

We present a study of localized transversal excitations in a system of weakly nonlinear oscillators coupled by linear bonds. The equations of motion are written in a complex form and then the multi-scale expansion is used. Short wave-length asymptotics have been considered. We have shown that in the case nonlinear Schrodinger equation (NSE) corresponds to the main approximation. This equation, in particular, possesses soliton-like solutions (breathers).