Controlled passage through resonance in mechanical systems

Methods of passing through resonance zones in mechanical systems are discussed and a new method based on the speed-gradient energy control of two subsystems (rotor and support) is presented. Two typical problems of passing through resonance for one- and two-dimensional motion of the support are posed and analyzed by computer simulation. The control algorithms based on the speed-gradient method and averaging allow one to significantly reduce the required level of the controlling torque. The proposed algorithms have a small number of design parameters. Compared with the known algorithms the proposed ones are more simple for design and exhibit stronger robustness properties.     

Pair-structure matrix of random collection of particles: Implications for light scattering

Scattering of light fields from random collections of particles of different types is considered. A new matrix called pair-structure matrix characterizing the correlations between particles of the same and of different types is introduced. This matrix reduces to the pair-structure factor of scattering collection [Opt. Lett. 34, 1762 (2009)] in the case when the particles in the collection are all of the same type. For illustration of the importance of the new matrix the formula for the degree of coherence of a polychromatic plane wave scattered from a collection of particles of different types is derived.     

How geometry controls the tearing of adhesive thin films on curved surfaces

Flaps can be detached from a thin film glued on a solid substrate by tearing and peeling. For flat substrates, it has been shown that these flaps spontaneously narrow and collapse in pointy triangular shapes. Here we show that various shapes, triangular, elliptic, acuminate, or spatulate, can be observed for the tears by adjusting the curvature of the substrate. From combined experiments and theoretical models, we show that the flap morphology is governed by simple geometric rules.     

Arrest of self-focusing collapse in femtosecond air filaments: higher order Kerr or plasma defocusing?

Experimentally measured conical emission rings on the blue side of the filament supercontinuum of a 800 nm 50 fs pulse in air are reproduced in simulations with plasma and the third-order Kerr as the nonlinear terms. This agreement indicates plasma as the dominant mechanism arresting the self-focusing collapse. The higher order Kerr terms with the recently measured coefficients stop the collapse at a lower intensity than the plasma does and lead to the spherical angle-wavelength spectrum without blueshifted rings.     

Technique for interaction of optical fields with turbulent medium containing particles

We develop a method for transmission of stochastic fields through turbulent media (atmosphere, ocean, biotissues) containing randomly distributed particles. The method is based on the angular spectrum representation of stochastic, statistically stationary, scalar fields, the Rytov perturbation series for propagation in weakly fluctuating media, and the first Born approximation for weak scattering from particulate media. The results for transmission of the deterministic (laser) field may be obtained from our general results as a limiting case.     

Iridium complexes of the doubly cyclometalated NHC ligand IMes'

Two consecutive C-H bond activations at the coordination sphere of Ir transform the commonly employed NHC ligand IMes into the new κ(3)-C fac-coordinating ligand IMes'. The preparation and structure of Ir(III) complexes featuring this ligand together with selected reactions toward small molecules that illustrate their reactivity keys are described.     

Coexisting tori and torus bubbling in non-smooth systems

Pulse modulated power electronic converters represent an important class of piecewise-smooth dynamical systems with a broad range of applications in modern power supply systems. The paper presents a detailed investigation of a number of unusual bifurcation phenomena that can occur in power converters with multilevel control. In the first example a closed invariant curve arises in a border-collision bifurcation as a period-6 saddle cycle collides with a stable fixed point of focus type and transforms it into an unstable focus point. The second example involves the formation of a structure of coexisting tori through the interplay between border-collision and global bifurcations. We examine the behavior of the system in the presence of two coexisting stable resonance tori and finally show how an existing torus can develop heteroclinic bubbles that connect the points of a stable resonance cycle with an external pair of saddle and focus cycles. The appearance of these structures is explained in terms of a sequence torus-birth bifurcations with pairs of stable and unstable tori folding one over the other.     

The laser polarization as control parameter in the formation of laser-induced periodic surface structures: Comparison of numerical and experimental results

Considering self-organized surface pattering upon multi-pulse femtosecond laser irradiation, in particularly the strong dependence of ripples orientation on the laser polarization, we present numerical simulations from an adopted surface erosion model and compare the result to our experimental data on laser-induced nanostructures formation. We present the surface morphologies obtained by this model for different polarizations of the incident laser electric field and show good agreement with ripple formation produced by laser ablation experiments. The correlation of ripples orientation with laser polarization can be described within a model where the polarization causes a breaking of symmetry at the surface. Further we discuss a time evolution of pattern formation. Our results support the non-linear self-organization mechanism of pattern formation on the surface of solids.     

Synthesis of Nitroxide Paramagnetic Ketones from Nitroxide Acid Chlorides and Anhydrides by Fiedel-Crafts Acylation

Friedel-Crafts acylation of benzene or toluene with 5- and 6-membered nitroxide acid chloride, anhydrides derivatives (symmetrical or mixed) and aluminium chloride to aryl nitroxide ketones is described.     

Ultrasound-Promoted Dimerization of Benzylic Halides

Simple and straightforward coupling of benzylic compounds was achieved by sonicating benzylic halides in the presence of magnesium.