Functional Carbazole Liquid‐Crystal Block Codendrimers with Optical and Electronic Properties

The synthesis and characterisation of a family of block codendrimers consisting of highly versatile mesogenic and carbazole‐containing 2,2‐bis(hydroxymethyl)propionic acid (bis‐MPA) dendrons are reported. The liquid‐crystal behaviour was investigated by means of differential scanning calorimetry, polarised‐light optical microscopy and X‐ray diffraction. Depending on the chemical structure of the constituent dendrons, the codendrimers show lamellar or columnar mesophases. On the basis of the experimental results, models both at the molecular level and in the mesophase are proposed. The physical properties of the block codendrimers derived from the presence of the carbazole moiety in their structure were investigated: photoluminescence in solution and in the mesophase, electrochemical behaviour and hole transport. Electrodeposition of carbazole dendrons afforded a globular supramolecular conformation in which the mesogenic molecular side plays a key role.     

Parametric Excitation for Two Internally Resonant van der Pol Oscillators

The response of a system of two nonlinearly coupled van der Poloscillators to a principal parametric excitation in the presence ofone-to-one internal resonance is investigated. The asymptoticperturbation method is applied to derive the slow flow equationsgoverning the modulation of the amplitudes and the phases of the twooscillators. These equations are used to determine steady-stateresponses, corresponding to a periodic motion for the starting system(synchronisation), and parametric excitation-response andfrequency-response curves. Energy considerations are used to studyexistence and characteristics of limit cycles of the slow flowequations. A limit cycle corresponds to a two-period amplitude- andphase-modulated motion for the van der Pol oscillators. Two-periodmodulated motion is also possible for very low values of the parametricexcitation and an approximate analytic solution is constructed for thiscase. If the parametric excitation increases, the oscillation period ofthe modulations becomes infinite and an infinite-period bifurcationsoccur. Analytical results are checked with numerical simulations.     

Bifurcation Analysis of Parametrically Excited Rayleigh–Liénard Oscillators

A parametrically excited Rayleigh–Liénard oscillator is investigatedby an asymptotic perturbation method based on Fourier expansion and timerescaling. Two coupled equations for the amplitude and the phase ofsolutions are derived and the stability of steady-state periodic solutionsas well as parametric excitation-response and frequency-response curvesare determined. Comparison with the parametrically excited Liénardoscillator is performed and analytic approximate solutions are checkedusing numerical integration. Dulac's criterion, thePoincaré–Bendixson theorem, and energy considerations are used in order to study the existence and characteristics of limit cycles of the twocoupled equations. A limit cycle corresponds to a modulated motion forthe Rayleigh–Liénard oscillator. Modulated motion can be also obtainedfor very low values of the parametric excitation, and in this case, anapproximate analytic solution is easily constructed. If the parametricexcitation is increased, an infinite-period bifurcation is observed because the modulation period lengthens and becomes infinite, while themodulation amplitude remains finite and suddenly the attractor settlesdown into a periodic motion. Floquet's theory is used to evaluatethe stability of the periodic solutions, and in certain cases,symmetry-breaking bifurcations are predicted. Numerical simulationsconfirm this scenario and detect chaos and unbounded motions in theinstability regions of the periodic solutions.     

The Dissipative Nonlocal Oscillator

The most important characteristics of a nonlocal and nonlinear oscillator subject to dissipative forces are extensively studied by means of an asymptotic perturbation method, based upon temporal rescaling and harmonic balance. The conditions under which bifurcations and limit cycles appear are determined. If the parameters satisfy particular conditions, a quasi-periodic motion is predicted, because a second small frequency adds to the natural frequency of the oscillator. The analytical results are validated by numerically solving the original system.     

The Response of an Oscillator Moving along a Parabola to an External Excitation

The behavior of a mass point moving along a parabola under theeffect of an external periodic excitation in resonance with the naturalfrequency of the oscillator is studied. The asymptotic perturbationmethod based on temporal rescaling and balancing of the harmonic termswith a simple iteration is used in order to determine the nonlinearmodulation equations for the amplitude and the phase of the oscillation.External force-response curves are shown and moreover jump phenomena arealso observed. In certain cases a second low frequency appears inaddition to the forcing frequency and then stable two-periodquasi-periodic motions are present with amplitudes depending on theinitial conditions. The value of the low frequency depends on theamplitude of the external excitation. A higher order perturbationanalysis is developed and the validity of the method is highlighted bycomparing the leading order and the higher order approximate analyticsolutions to numerical results.     

Water evaporation from gel beads

Hydrogels are characterized by properties which make them ideal candidates for applications in several fields, such as drug delivery, biomedicine, and functional foods. Molecular diffusion out of a hydrogel matrix depends on their hydrodynamic radii and the mesh sizes within the matrix of the gel. A quantitative experimental and mathematical understanding of interactions, kinetics, and transport phenomena within complex hydrogel systems assists network design by identifying the key parameters and mechanisms that govern the rate and extent of solute release. In this article a calorimetric differential scanning calorimetry (DSC) study reports on the approach to parallel water effusion from a hydrogel matrix to the release of a model protein. The measurement of the water evaporation is taken as the simplest routine determination of a phenomenon that is basically due to a diffusive process through the porous structure of the gel and thermodynamically governed by the difference in the water chemical potential inside and outside of the bead. The analysis of the experimental calorimetric curves is made with the purpose of extracting several numerical parameters characteristic of each curve. The rationale is to develop a simple methodology to understand the release properties of the porous structure of the complex gel matrix by means of DSC.     

Determination of hydrazine in drinking water: Development and multivariate optimization of a rapid and simple solid phase microextraction-gas chromatography-triple quadrupole mass spectrometry protocol

In this work, the capabilities of solid phase microextraction were exploited in a fully optimized SPME-GC-QqQ-MS analytical approach for hydrazine assay. A rapid and easy method was obtained by a simple derivatization reaction with propyl chloroformate and pyridine carried out directly in water samples, followed by automated SPME analysis in the same vial without further sample handling. The affinity of the different derivatized compounds obtained towards five commercially available SPME coatings was evaluated, in order to achieve the best extraction efficiency. GC analyses were carried out using a GC-QqQ-MS instrument in selected reaction monitoring (SRM) acquisition mode which has allowed the achievement of high specificity by selecting appropriate precursor–product ion couples improving the capability in analyte identification. The multivariate approach of experimental design was crucial in order to optimize derivatization reaction, SPME process and tandem mass spectrometry parameters. Accuracy of the proposed protocol, tested at 60, 200 and 800 ng L⁻¹, provided satisfactory values (114.2%, 83.6% and 98.6%, respectively), whereas precision (RSD%) at the same concentration levels were of 10.9%, 7.9% and 7.7% respectively. Limit of detection and quantification of 4.4 and 8.3 ng L⁻¹ were obtained. The reliable application of the proposed protocol to real drinking water samples confirmed its capability to be used as analytical tool for routine analyses.     

On chaotic extensions of dynamical systems

In this paper, inspired by some results in linear dynamics, we will show that every dynamical system (X,f), where f is a continuous self-map on a separable metric space X, can be extended to a chaotic (in the sense of Devaney) dynamical system in an isometric way.     

Vibration control by nonlocal feedback and jerk dynamics

Jerk dynamics is used for a new method for the suppression of self-excited vibrations in nonlinear oscillators. Two cases are considered, the van der Pol equation and nonlinear oscillator with quadratic and cubic nonlinearities. A nonlocal control force is introduced in such a way to obtain a third order nonlinear differential equation (jerk dynamics). Using the asymptotic perturbation method, two slow flow equations on the amplitude and phase of the response are obtained, and subsequently the performance of the control strategy is investigated. The feedback gains are connected with the stability and response of the system under control. Uncontrolled and controlled systems are compared and the appropriate choices for the feedback gains are found in order to reduce the amplitude peak of the self-excitations. Numerical simulation confirms the validity of the new method.