Predicting Homoclinic Bifurcations in Planar Autonomous Systems

An analytical method to predict the homoclinic bifurcation in a planar autonomous self-excited weakly nonlinear oscillator is presented. The method is mainly based on the collision between the periodic orbit undergoing the homoclinic bifurcation and the saddle fixed point. To illustrate the analytical predictive criteria, two typical examples are investigated. The results obtained in this work are then compared to Melnikov's technique and to a previous criterion based on the vanishing of the frequency. Numerical simulations are also provided.     

Viscoelastic properties and interfacial tension of polystyrene–polyethylene blends

The linear viscoelastic properties of polystyrene polyethylene (PS/PE) blends have been investigated in the molten state. For concentrations of the dispersed phase equal to 30 vol %, the blends exhibited a droplet‐matrix morphology with a volume‐average diameter of 5.5 μm for a 70/30 PS/PE blend at 200 °C and 14.7 μm for a 30/70 PS/PE blend at 230 °C. Enhanced elasticity (G′) for both blends, in the terminal zone, compared to the modulus of the matrix (PS and PE, respectively) was observed. This is related to the deformation of the droplets in the matrix phase and hence to the interfacial forces between the blend components. The results for these uncompatibilized blends are shown to be in agreement with the predictions of the emulsion model of Palierne. These predictions were used to obtain the interfacial tension between PS and PE, which was found to be between 2 and 5 mN/m at 200 °C and 4 ± 1 mN/m at 230 °C. Independent interfacial tension measurements using the breaking‐thread method resulted in a value of 4.7 mN/m and 4.1 mN/m at 200 °C and 230 °C for the respective blends. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1359–1368, 2000     

Effect of rheological and physical properties on mitigation of melt fracture instability during extrusion of polymer melts through a radial flow die

This study examines the role of both a radial flow created at the entrance of the die and the average molecular weight of polymer on the appearance and development of the helical defect. To do so, three linear polydimethylsiloxanes (PDMSs) of different viscosities and molecular weights were considered. A convergent radial flow is created at the entrance zone when a radial geometry is generated upstream the extrusion die. As for the influence of the considered radial flow, extrudate photographs show that helical instability can be mitigated since its frequency is higher and its amplitude is smaller than what they are when radial flow geometry is not installed. However, it is possible to relate the observed effects to the establishment of the radial flow at the die entrance where the shear deformations are enhanced with respect to the elongational ones. In fact, the development of the helical defect is shaped with amplitude, which is sensitive to the gap width of the radial flow and a frequency imposed by both the entrance geometry and the molecular weight of the polymer. It has also been shown that the ratio of frequencies of the onset of helical instability and the ratio of the Newtonian viscosities, for two given polymers, are inversely equal. Moreover, results obtained confirm that the frequency of the instabilities at their onset is inversely proportional to a mean characteristic time τ _M as to the plateau viscosity of the considered PDMS.     

Suppression of hysteresis in a forced van der Pol–Duffing oscillator

This paper examines the suppression of hysteresis in a forced nonlinear self-sustained oscillator near the fundamental resonance. The suppression is studied by applying a rapid forcing on the oscillator. Analytical treatment based on perturbation analysis is performed to capture the entrainment zone, the quasiperiodic modulation domain and the hysteresis area as well. The analysis leads to a strategy for the suppression of hysteresis occurring between 1:1 frequency-locked motion and quasiperiodic response. This hysteresis suppression causes the disappearance of nonlinear effects leading to a smooth transition between the quasiperiodic and the frequency-locked responses. Specifically, it appears that a rapid forcing introduces additional apparent nonlinear stiffness which can effectively suppress hysteresis in a certain range of the rapid excitation frequency. This work was motivated by the important issue of controlling and eliminating hysteresis often undesirable in mechanical systems, in general, and in application to microscale devices, especially.     

Supermolecular chiral mesogenic tripedes

A novel series of chiral liquid crystalline tripedes Glucoside and Mannoside derivatives G(n) and M(n) (n=1-3) have been synthesised. The inner cores consist of methyl α-D-Glucoside G or methyl α-D-Mannoside M, regioselectively functionalised at the less hindered position C6, with tert-butyldimethylsilyl (TBDMS), hydroxyl or carboxylic acid moieties. The cores, which can acquire several flexible conformations, are attached to rod-like smectogenic-preferring cyanobiphenyl units, by means of a flexible hexanoyl spacer. These Glyco-Supermolecules exhibit chiral nematic (N*) and smectic A (SmA) phases. The combined effects of core chirality and functional groups on thermal and mesomorphic characteristics are discussed.     

Variational problem in the non-negative orthant of ℝ<Superscript>3</Superscript>: reflective faces and boundary influence cones

In this paper we consider the variational problem in the non-negative orthant of ℝ³. The solution of this problem gives the large deviation rate function for the stationary distribution of an SRBM (Semimartingal Reflecting Brownian Motion). Avram, Dai and Hasenbein (Queueing Syst. 37, 259–289, 2001) provided an explicit solution of this problem in the non-negative quadrant. Building on this work, we characterize reflective faces of the non-negative orthant of ℝ ^d , we construct boundary influence cones and we provide an explicit solution of several constrained variational problems in ℝ³. Moreover, we give conditions under which certain spiraling paths to a point on an axis have a cost which is strictly less than the cost of every direct path and path with two pieces.     

2:1 and 1:1 frequency-locking in fast excited van der Pol–Mathieu–Duffing oscillator

The frequency-locking area of 2:1 and 1:1 resonances in a fast harmonically excited van der Pol–Mathieu–Duffing oscillator is studied. An averaging technique over the fast excitation is used to derive an equation governing the slow dynamic of the oscillator. A perturbation technique is then performed on the slow dynamic near the 2:1 and 1:1 resonances, respectively, to obtain reduced autonomous slow flow equations governing the modulation of amplitude and phase of the corresponding slow dynamics. These equations are used to determine the steady state responses, bifurcations and frequency-response curves. Analysis of quasi-periodic vibrations is carried out by performing multiple scales expansion for each of the dependent variables of the slow flows. Results show that in the vicinity of both considered resonances, fast harmonic excitation can change the nonlinear characteristic spring behavior from softening to hardening and causes the entrainment regions to shift. It was also shown that entrained vibrations with moderate amplitude can be obtained in a small region near the 1:1 resonance. Numerical simulations are performed to confirm the analytical results.     

Removal of Malachite Green Dye from Aqueous Solution by Catalytic Wet Oxidation Technique Using Ni/Kaolin as Catalyst

In this study, natural Algerian kaolin was used as a support and impregnated with nickel at different loading amounts (2 wt.%, 5 wt.%, and 7 wt.%) in order to prepare a supported catalyst. The wet impregnation technique was used in this preparation; nickel oxide (NiO) was the active phase precursor of the catalyst, and the catalysts were designated as follows: 2%, 5%, and 7% Ni/kaolin. These catalysts were put to the test in catalytic wet peroxide oxidation (CWPO) for degrading the organic contaminant malachite green dye (MG). Analytical techniques such as FTIR spectroscopy, X-ray diffraction, BET, and X-fluorescence were used to examine the structure, morphology, and chemical composition of the support and the produced catalysts. Several parameters, including temperature, catalytic dose, metal loading, hydrogen peroxide volume, and kinetic model were systematically investigated. The combination of improved parameters resulted in a significant increase in the catalytic activity, achieving a high removal rate of MG dye of 98.87%.     

Retrodienic reactions XVII - a general route to allenes gem-diactivated by electroattracting groups

Ketone 6 undergoes Knoevenagel condensation with five malonic derivatives 7, yielding, after flash-thermolysis, the gem-diactivated allenes 1–5 in 20–50 % yields.     

Improvement and application of two extrapolation methods to FT-IR data

The applicability of two non-parametric extrapolation methods to FT-IR absorptance spectra is investigated. The first method minimizes those parts of the spectrum which do not satisfy a given constraint, while the second one changes them in each iteration through the true values.