Bifurcation phenomena near homoclinic systems: A two-parameter analysis

The bifurcations of periodic orbits in a class of autonomous three-variable, nonlinear-differential-equation systems possessing a homoclinic orbit associated with a saddle focus with eigenvalues ( ±i,), where ¦/¦ < 1 (Sil'nikov's condition), are studied in a two-parameter space. The perturbed homoclinic systems undergo a countable set of tangent bifurcations followed by period-doubling bifurcations leading to periodic orbits which may be attractors if ¦/¦ < 1/2. The accumulation rate of the critical parameter values at the homoclinic system is exp(-2¦/¦). A global mechanism for the onset of homoclinicity in strongly contractive flows is analyzed. Cusp bifurcations with bistability and hysteresis phenomena exist locally near the onset of homoclinicity. A countable set of these cusp bifurcations with scaling properties related to the eigenvalues±i of the stationary state are shown to occur in infinitely contractive flows. In the two-parameter space, the periodic orbit attractor domain exhibits a spiral structure globally, around the set of homoclinic systems, in which all the different periodic orbits are continuously connected.     

Application of the JKR Method to the Measurement of Adhesion to Langmuir-Blodgett Cellulose Surfaces

The JKR method has been applied for studying adhesion between poly(dimethylsiloxane) (PDMS) caps and Langmuir–Blodgett cellulose surfaces including the substrate, hydrophobized mica, and two flat mineral surfaces, bare mica and glass. The self-adhesion of PDMS caps and oxidized PDMS caps are included as a reference to compare with literature data. The results of the measurements have been compared with previous studies using the surface force apparatus and similar systems. A satisfactory agreement is obtained for simple systems showing no, or very limited, hysteresis between loading and unloading curves. In several cases, however, a large hysteresis is found between loading and unloading curves, with a larger adhesion measured from the pull-off force than from the JKR-curve determined on loading. This is, for instance, the case for PDMS against cellulose. The situation is analogous to that found in wetting studies showing a large hysteresis between advancing and receding contact angles.     

Mechanism of the molecular hysteresis

The redox behavior in acetone solution of (1,5-dithiacyclooctane 1-oxide)bis(pentaammineruthenium(II)) has been characterized, where the concept of “molecular hysteresis” is presented. Detailed thermodynamics for the complex are studied, in which intramolecular electron transfer rates for Ru³⁺OS/Ru²⁺→Ru²⁺SO/Ru³⁺ were determined as 0.12 sec^?1 and 0.055 sec^?1. The molecular hysteresis consists of two important factors: isomerizations for the sulfoxideruthenium complexes and the slow intramolecular electron transfer in the complex; both are examined. Isomerization rates for Ru³⁺S→O and Ru²⁺O→S determined range from 0.4 to 5000 sec^?1 and from 0.7 to 16 sec^?1, respectively, for [Ru(NH₃)₅(sulfoxide)]^2+/3+. A mechanism for the slow electron transfer in the complex is also presented. Features of molecular hysteresis are discussed.     

ELASTIC BEHAVIOR OF PROTEIN-LIKE SINGLE CHAIN

The conformational properties and elastic behaviors of protein-like single chains in the process of tensile elongation were investigated by means of Monte Carlo method. The sequences of protein-like single chains contain two types of residues: hydrophobic (H) and hydrophilic (P). The average conformations and thermodynamics statistical properties of protein-like single chains with various elongation ratio λ were calculated. It was found that the mean-square end-to-end distance r increases with elongation ratio,λ. The tensor eigenvalues ratio of : decreases with elongation ratio λ for short (HP)x protein-like polymers, however, the ratio of : increases with elongation ratioλ,especially for long (H)x sequence. Average energy per bond increases with elongation ratioλ, especially for(H)x protein-like single chains. Helmholtz free energy per bond also increases with elongation ratioλ. Elastic force (f), energy contribution to force (fU) and entropy contribution to force (fs) for different protein-like single chains were also calculated.These investigations may provide some insights into elastic behaviors of proteins.     

Modulated differential scanning calorimetry in the glass transition region

Temperature-modulated calorimetry (TMC) allows the experimental evaluation of the kinetic parameters of the glass transition from quasi-isothermal experiments. In this paper, model calculations based on experimental data are presented for the total and reversing apparent heat capacities on heating and cooling through the glass transition region as a function of heating rate and modulation frequency for the modulated differential scanning calorimeter (MDSC). Amorphous poly(ethylene terephthalate) (PET) is used as the example polymer and a simple first-order kinetics is fitted to the data. The total heat flow carries the hysteresis information (enthalpy relaxation, thermal history) and indications of changes in modulation frequency due to the glass transition. The reversing heat flow permits the assessment of the first and higher harmonics of the apparent heat capacities. The computations are carried out by numerical integrations with up to 5000 steps. Comparisons of the calculations with experiments are possible. As one moves further from equilibrium, i.e. the liquid state, cooperative kinetics must be used to match model and experiment.On leave from Toray Industries, Inc., Otsu, Shiga 520, Japan.This work was supported by the Division of Materials Research, National Science Foundation, Polymers Program, Grant # DMR 90-00520 and the Division of Materials Sciences, Office of Basic Energy Sciences, U. S. Department of Energy at Oak Ridge National Laboratory, managed by Lockheed Martin Energy Research Corp. for the U. S. Department of Energy, under contract number DE-AC05-96OR22464. Support for instrumentation came from TA Instruments, Inc. Research support was also given by ICI Paints, and Toray Industries, Inc.     

Ionization potential of excited states of Be‐like sequence in the concept of iso‐spectrum‐level series

With the introduction of the concept of the iso‐spectrum‐level series, a linear relationship is found between the first differences of the ionization potential of excited states and nuclear charge Z along an iso‐spectrum‐level series, and the ionization potential of excited states of Be‐like sequence are studied systematically on the basis of the weakest bound electron potential model theory. The expression of nonrelativistic ionization potential is derived from the weakest bound electron potential model theory, and relativistic effects are included by using a fourth‐order polynomial in Z. As a demonstration, the ionization potentials of [He]2s2p ³P, [He]2s3s ¹S₀, [He]2s3p ¹P, [He]2s3d ¹D₂, and [He]2s4d ¹D₂ series for a range of Be‐like sequence from Z = 4–23 are calculated. The results are compared with the experimental data and the recent sophisticated ab initio results. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 344–350, 2003     

Allowed transitions in silicon isoelectronic ions

Dipole‐allowed transitions have been studied for the first few members of the Si isoelectronic sequence. Transition energies, oscillator strengths, transition probabilities and quantum defect values have been estimated for the low‐ and high‐lying excited states of s and d symmetries up to the principal quantum number n=7 for these 3p open shell ions from P⁺ to Cr¹⁰⁺. Time‐dependent coupled Hartree–Fock (TDCHF) theory has been utilized to calculate such transition properties. Most of the results for transition energies, oscillator strengths, and transition probabilities for higher excited states are new. The transition energies for low‐lying excited states agree well with experimental data wherever available. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Polyaniline films doped with zinc salts and their properties

It has been found that thin polyaniline films doped with several zinc salts in solutions at pH 5.5 become electroconductive and electroactive in neutral aqueous electrolytes. The shape of the voltammetric characteristics depends on the initial state of the film. The effect of secondary doping withm-cresol is observed for polyaniline complexes with zinc salt of camphorsulfonic acid.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1450–1452, June, 1996.     

表面图案化磁性复合微球的原位制备与表征

采用反相悬浮聚合法合成了丙烯酸(AA)含量不同的N-异丙基丙烯酰胺-丙烯酸共聚物P(NIPAM-co-AA)微凝胶, 并以其作为微反应器, 通过原位外源沉积法制备了一系列微米级、表面具有图案化结构的SiO₂-Fe₃O₄-P(NIPAM-co-AA)磁性复合微球. 实验结果表明, 复合微球的表面结构与微凝胶的组成、Fe₃O₄和SiO₂的沉积量有关. 在微球表面进行修饰, 可得到表面带有氨基等官能基团的磁性复合材料. 将这种功能化磁性微球用于识别生物大分子并进一步用于生物医学领域具有重要的意义.