Some aspects of destabilization in reversible dynamical systems with application to follower forces

This paper examines the destabilization of the equilibria of reversible dynamical systems which is induced by the addition of irreversible perturbations. Attention is restricted to reversible dynamical systems which have frequently appeared in the literature on elastic stability. There they are often referred to as follower force problems. The destabilization phenomenon is linear in nature and explicit criteria are established to determine the particular eigenvalue splittings. The post-destabilization dynamics are also examined using the appropriate normal forms for two specific cases, one where the eigenvalues are non-resonant and the other where the eigenvalues are in a strong one-to-one resonance. Finally, the destabilization criteria and certain features of the post-destabilization dynamics are illustrated using two examples of follower force systems.     

Ultrasonic Modification of Polymers. I. Degradations of Polystyrene in the Presence of Various Poly(alkyl Methacrylates)

Ultrasonic (70 W, 20 kHz) degradations of polystyrene (PS) have been carried out with various poly(alkyl methacrylates) (PRMA) for periods of 3 h at 27°C in toluene (2.0 to 5.0% solutions). The isolation of sequence copolymers thus prepared from their associated homopolymers was achieved by employing selective solvents (solvent for one homopolymer but a precipitant for the second homopolymer in the mixture). The recovered products were analyzed by gel permeation chromatography (GPC), infrared spectroscopy (IR), and viscometry. These analyses showed that when the substituents in PRMA were methyl, ethyl, isopropyl, n-butyl, isobutyl, or phenyl, sequence copolymers with segments from PS as well as from poly(alkyl methacrylate) were obtained. However, when the substituents on PRMA were hexyl, isodecyl, lauryl, hexadecyl, octadecyl or isobornyl there were no sequence copolymers formed. The decrease in the intrinsic viscosity of the recovered homopolymers and shifts of their GPC chromatograms toward the low molecular weight end suggest that on sonification PRMA samples having bulkier substituents do degrade and yield radicals which, however, do not recombine with those from polystyrene. Furthermore, ultrasonic degradation of polystyrene is found to be dependent on the chain stiffness of the poly(alkyl methacrylates).     

Polymerization of α-Methylstyrene in Cyclohexane with Potassium as Initiator. IV. Thermodynamic Study and Gel-Permeation Chromatographic Analyses of the Polymers

Polymerization of α-methylstyrene in cyclohexane containing traces of tetrahydrofuran (THF) has been carried out at 40°C with potassium as initiator. The conversion of monomer to polymer was very slow, and a solution with [M]₀ of 5.15 mole/ liter, carrying 0.110 mole/liter of the living ends [LE], required two months to reach a stationary state. The gel-permeation chromatographic (GPC) analyses of these polymers showed them to have multimodal distributions which could be split into components D+A, B, and C similar to those found for poly-α-methylstyrene prepared in THF and α-dioxane as solvents. Furthermore, under identical conditions of [M]₀ and [LE], the GPC distributions of poly-α-methylstyrene prepared in cyclohexane, p-dioxane, and THF were the same, in spite of their different dielectric constants. Under identical conditions of [M]₀ but with different [LE], the effect of excessive [LE] on the GPC distributions of the polymers prepared in cyclohexane was not limited to the component D+A as was the case when THF or p-dioxane were the solvents, but also on the component C which increased its contribution [P]_e to the polymer.     

Energetics of the Acid-Catalyzed o-Cresol-Formaldehyde Reaction

The acid-catalyzed reaction of o-cresol with formaldehyde follows second-order kinetics. The reaction was carried out at 65, 70, 75, and 80°C and at pH values of 1.30, 1.80, 2.00, 2.50, and 3.00, using hydrochloric acid as a catalyst. The rate was found to increase with decreasing pH. The overall rate constant (k) has been resolved into stepwise rate constants (k₁ and k₂) for the formation of monomethylol and methylene derivatives. Values of Arrhenius parameters and of the entropy of activation for the overall reaction were also calculated. A mechanism consistent with our kinetic data is given.     

Anionic Polymerization of α-Methylstyrene. IX. Nature of the Propagating Species

Abstract

The nature of the initiating and propagating species involved in the anionic polymerization of α-methylstyrene has been explored. The earlier hypothesis that multimodal GPC molecular weight distributions in polymers arise solely out of different reaction steps or different ion-pair mechanisms being involved has been modified for poly-α-methylstyrene. Multimodal GPC molecular weight distributions in poly-α-methylstyrene initiated with potassium at 25°C and polymerized at 25°C or higher in THF, p-dioxane, or cyclohexane as solvents have been ascribed to the presence of two different types of tetramers which grow simultaneously but at different rates, each responding to its own well-defined thermodynamic equilibrium and yielding dormant and living polymers. Reaction schemes describing the initiation (at 25°C) and propagation reactions (between -25 and 60°C) in the polymerization (in solution of THF as well as in bulk) of α-methylstyrene initiated with potassium-naphthalene, butyl-lithium, and butyllithium-tetramethylethylenediamine (TMEDA) have been presented. The role of coordinating agents naphthalene and TMEDA in changing irreversible propagations into reversible ones has been emphasized.     

Compensating spectral loss variations in EDFA amplifiers for different modulation formats

In this paper, we investigate the performance of the optical system consisting of chain of EDFA amplifiers for different data formats such as non-return-to-zero (NRZ), return to zero (RZ) and Manchester. Their effect on the spectral loss variations produced in fiber output is analyzed. We show that when the RZ raised cosine and Manchester raised cosine modulation formats are used, the non-linear ties are produced in power spectrum plots which severely distort the signals obtained at the output of the chain of the EDFA amplifiers. On the other hand, the NRZ raised cosine modulation format best compensates the spectral loss variations in the power spectrum plots obtained at the output. We further show that NRZ raised cosine has good eye opening as compared to other modulation formats.     

A Highly Efficient and Broadly Applicable Cationic Gold Catalyst

Gold catalysts capable of promoting reactions at low‐level loadings under mild conditions are the exception rather than the norm. We examined reactions where the regeneration of cationic gold catalyst (e.g., protodeauration) was the turnover limiting stage. By manipulating electron density on the substituents around phosphorus and introducing steric handles we designed a phosphine ligand that contains two electron‐rich ortho‐biphenyl groups and a cyclohexyl substituent. This ligand formed a gold complex that catalyzed common types of gold‐catalyzed reactions including intra‐ and intermolecular X? H (X=C, N, O) additions to alkynes and cycloisomerizations, with high turnover numbers at room temperature or slightly elevated temperatures (≤50 °C). Our new ligand can be prepared in one step from commercially available starting materials.     

Energy dependence of multiplicity in proton-nucleus collisions and models of multiparticle production

This is a continuation of our earlier investigation (Gurtuet al 1974Phys. Lett. 50 B 391) on multiparticle production in proton-nucleus collisions based on an exposure of emulsion stack to 200 GeV/c beam at the NAL. It is found that the ratioR _em = 〈n _s〉/〈n _ch〉, where 〈n _ch〉 is the charged particle multiplicity in pp-collisions, increases slowly from about 1 at 10 GeV/c to 1·6 at 68 GeV/c and attains a constant value of 1·71 ± 0·04 in the region 200 to 8000 GeV/c. Furthermore,R _em = 1·71 implies an effectiveA-dependence ofR _A =A ^0.18,i.e., a very weak dependence. Predictions ofR _em on various models are discussed and compared with the emulsion data. Data seem to favour models of hadron-nucleon collisions in which production of particles takes place through adouble step mechanism,e.g., diffractive excitation, hydrodynamical and energy flux cascade as opposed to models which envisage instantaneous production.