Long Term Stability of Proper Rotations of the Perturbed Euler Rigid Body

We study the long term stability of the proper rotations of the perturbed Euler rigid body, in the framework of Nekhoroshev theory. For simplicity we treat here in detail only the kinetically symmetric case (the potential needs not to be symmetric), but we indicate how to extend the results to the triaxial case. We show that the proper rotations around the symmetry axis are Nekhoroshev stable: more precisely, if the initial datum is sufficiently close to a proper rotation, then for a very long time it remains such, and the tip of the unit vector parallel to the angular momentum precesses, up to a small noise, along the level curves of a regular function on the unit sphere. If the proper rotations are resonant, chaotic motions with positive Lyapunov exponents are possible, but chaos (unlike the case of ordinary motions, that is motions not close to proper rotations) is always localized, and does not affect in an essential way the motion of the angular momentum in space. Preliminary numerical results indicate that the theory is, in many aspects, optimal, although in some points it can still be improved.     

A solid-phase approach towards the development of 3-aza-6,8-dioxabicyclo[3.2.1]octane scaffolds

The development of new strategies for solid-phase synthesis of 3-aza-6,8-dioxabicyclo[3.2.1]octane scaffolds, named BTKa, is described. The preparation was made possible by the combination of three components: amines, alpha-halo-acetophenones, and sugar or tartaric acid derivatives. By anchoring each of the three components it was possible to synthesize BTKa compounds either as amino alcohols or amido esters. The compatibility of the protocols with different classes of amines and substituted alpha-halo-acetophenones was demonstrated.     

Scaling exponents and probability distributions of DNA end-to-end distance

The scaling of the average gyration radius of polymers as a function of their length can be experimentally determined from ensemble measurements, such as light scattering, and agrees with analytical estimates. Ensemble techniques, yet, do not give access to the full probability distributions. Single molecule techniques, instead, can deliver information on both average quantities and distribution functions. Here we exploit the high resolution of atomic force microscopy over long DNA molecules adsorbed on a surface to measure the average end-to-end distance as a function of the DNA length, and its full distribution function. We find that all the scaling exponents are close to the predicted 3D values (upsilon=0.589+/-0.006 and delta=2.58+/-0.77). These results suggest that the adsorption process is akin to a geometric projection from 3D to 2D, known to preserve the scaling properties of fractal objects of dimension df<2.     

A kinetic Monte Carlo method on super-lattices for the study of the defect formation in the growth of close packed structures

A modified Kinetic Lattice Monte Carlo model has been developed to predict growth rate regimes and defect formation in the case of the homo-epitaxial growth of close packed crystalline structures. The model is an improvement over standard Monte Carlo algorithms, which usually retain fixed atom positions and bond partners indicative of perfect crystal lattices. Indeed, we extend the concepts of Monte Carlo growth simulations on super-lattices containing additional sites (defect sites) with respect to those of the reference material. This extension implies a reconsideration of the energetic mapping, which is extensively presented, and allows to describe a complex phenomenology that is out of accessibility of standard stochastic approaches. Results obtained using the Kawasaki and the Bond-Counting rules for the transition probability of the Monte Carlo event are discussed in details. These results demonstrate how the defect types (local or extended), the formation mechanisms and the defect generation regimes can be characterized using our approach.     

Continuously spacing-tunable multiwavelength semiconductor-optical-amplifier-based fiber ring laser incorporating a superimposed chirped fiber Bragg grating

We investigate a flexibly tunable multiwavelength semiconductor-optical-amplifier-based fiber ring laser with continuous wavelength spacing controllability incorporating a superimposed chirped fiber Bragg grating (CFBG). The wavelength spacing of a superimposed CFBG can be continuously controlled by symmetrically modifying the chirp bandwidth of the grating with the specially designed apparatus. We achieve a wide and continuous tuning range of the wavelength spacing from 0.35 to 0.78 nm. The continuous tunability of the wavelength spacing is measured to be ~ +/-0.033 nm/mm. By controlling the reflection bandwidth of the tunable CFBG, we can independently adjust the number of lasing channels from 2 to 23 at the wavelength spacing of 0.51 nm.     

Mean-field gauge interactions in five dimensions II. The orbifold

We study Gauge–Higgs Unification in five dimensions on the lattice by means of the mean-field expansion. We formulate it for the case of an SU(2)$\mathit{SU}(2)$ pure gauge theory and orbifold boundary conditions along the extra dimension, which explicitly break the gauge symmetry to U(1)$U(1)$ on the boundaries. Our main result is that the gauge boson mass computed from the static potential along four-dimensional hyperplanes is non-zero implying spontaneous symmetry breaking. This observation supports earlier data from Monte Carlo simulations in Irges and Knechtli (2007) [12].     

The influence of track modelling options on the simulation of rail vehicle dynamics

This paper investigates the effect of different models for track flexibility on the simulation of railway vehicle running dynamics on tangent and curved track. To this end, a multi-body model of the rail vehicle is defined including track flexibility effects on three levels of detail: a perfectly rigid pair of rails, a sectional track model and a three-dimensional finite element track model. The influence of the track model on the calculation of the nonlinear critical speed is pointed out and it is shown that neglecting the effect of track flexibility results in an overestimation of the critical speed by more than 10%. Vehicle response to stochastic excitation from track irregularity is also investigated, analysing the effect of track flexibility models on the vertical and lateral wheel–rail contact forces. Finally, the effect of the track model on the calculation of dynamic forces produced by wheel out-of-roundness is analysed, showing that peak dynamic loads are very sensitive to the track model used in the simulation.     

Adaptive behaviour of the spinal cord in the transition from quiet stance to walking

Background

Parkinson??s disease is characterized by a continuous loss of neurons within the substantia nigra (SN) leading to a depletion of dopamine. Within the adult SN as a non-neurogenic region, cells with mainly oligodendrocytic precursor characteristics, expressing the neuro-glial antigen-2 (NG2) are continuously generated. Proliferation of these cells is altered in animal models of Parkinson??s disease (PD). Exercise and environmental enrichment re-increase proliferation of NG2⁺ cells in PD models, however, a possible mechanistic role of dopamine for this increase is not completely understood. NG2⁺ cells can differentiate into oligodendrocytes but also into microglia and neurons as observed in vitro suggesting a possible hint for endogenous regenerative capacity of the SN. We investigated the role of dopamine in NG2-generation and differentiation in the adult SN stimulated by physical activity and environmental enrichment.

Results

We used the 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP)-model for dopamine depletion and analysed newborn cells in the SN at different maturation stages and time points depending on voluntary physical activity, enriched environment and levodopa-treatment. We describe an activity- induced increase of new NG2-positive cells and also mature oligodendrocytes in the SN of healthy mice. Running and enriched environment refused to stimulate NG2-generation and oligodendrogenesis in MPTP-mice, an effect which could be reversed by pharmacological levodopa-induced rescue.

Conclusion

We suggest dopamine being a key regulator for activity-induced generation of NG2-cells and oliogodendrocytes in the SN as a potentially relevant mechanism in endogenous nigral cellular plasticity.     

Periodic orbits, damped transitions and targeted energy transfers in oscillators with vibro-impact attachments

We study complex damped and undamped dynamics and targeted energy transfers (TETs) in systems of coupled oscillators, consisting of single-degree-of-freedom primary linear oscillators (LOs) with vibro-impact attachments, acting, in essence, as vibro-impact nonlinear energy sinks (VI NESs). First, the complicated dynamics of such VI systems is demonstrated by computing the VI periodic orbits of underlying Hamiltonian systems and depicting them in appropriate frequency–energy plots (FEPs). Then, VI damped transitions and distinct ways of passive TETs from the linear oscillators to the VI attachments for various parameter ranges and initial conditions are investigated. As in the case of smooth stiffness nonlinearity [Y. Lee, G. Kerschen, A. Vakakis, P. Panagopoulos, L. Bergman, D.M. McFarland, Complicated dynamics of a linear oscillator with a light, essentially nonlinear attachment, Physica D 204 (1–2) (2005) 41–69], both fundamental and subharmonic TET can be realized in the VI systems under consideration. It is found that the most efficient mechanism for VI TET is through the excitation of highly energetic VI impulsive orbits (IOs), i.e., of periodic or quasiperiodic orbits corresponding to zero initial conditions except for the initial velocities of the linear oscillators. In contrast to NESs with smooth essential nonlinearities considered in previous works, VI NESs are capable of passively absorbing and locally dissipating significant portions of the energies of the primary systems to which they are attached, at fast time scale. This renders such devices suitable for applications, like seismic mitigation, where dissipation of vibration energy in the early, highly energetic regime of the motion is a critical requirement.     

Playing with Numbers, with Fermions and Bosons

We construct nonlinear maps which realize the fermionization of bosons and the bosonization of fermions with the view of obtaining states coding naturally integers in standard or in binary basis. Specifically, with reference to spin systems, we derive raising and lowering bosonic operators in terms of standard fermionic operators and vice versa. The crucial role of multiboson operators in the whole construction is emphasized. Dedicated to Giuseppe Castagnoli for his 65th birthday.