Entropy Unilateral Solution for Some Noncoercive Nonlinear Parabolic Problems Via a Sequence of Penalized Equations

We give an existence result of the obstacle parabolic equations(b(x,u))/(t)-div(a(x,t,u,▽u))+div(φ(x,t,u))=f in Q_T,where b(x,u) is bounded function of u,the term-div(a(x,t,u,▽u)) is a Leray-Lions type operator and the function φ is a nonlinear lower order and satisfy only the growth condition.The second term f belongs to L~1(Q_T).The proof of an existence solution is based on the penalization methods.     

复微分-差分方程组的超越整函数解

利用亚纯函数的Nevanlinna值分布理论, 我们主要研究了一类复微分-差分方程和一类复微分-差分方程组的有限级超越整函数解的存在形式, 得到两个有趣的结论. 将复微分(差分)方程的一些结论推广到复微分-差分方程(组)中.     

The Value Distribution and Normality Criteria of a Class of Meromorphic Functions

In this article, we use Zalcman Lemma to investigate the normal family of meromorphic functions concerning shared values, which improves some earlier related results.     

Analytical Modelling of Electron-coupled Ion Transfers with Immobilized vs Soluble Redox Transducer at Thick Film-modified Electrodes

Analytical theoretical solutions are deduced for the current-potential response, concentration profiles and interfacial potentials of electron-coupled ion transfers in the cyclic voltammetry with thick film-modified electrodes. The theory covers a wide variety of possible situations, namely, the redox transducer can be either immobilized on the working electrode or freely diffusing in the organic film, and the ion transfer can be either simple or complicated by homogeneous chemical processes. A comparative and comprehensive study of each case is performed, establishing the key parameters that define the behaviour of the system, as well as guidelines to analyse its electrochemical signal.     

Ternary mutual diffusion coefficients of aqueous {l-dopa (1) + β-CD (2)} solutions at T = 298.15 K

Ternary mutual diffusion coefficients (D₁₁, D₂₂, D₁₂ and D₂₁) measured by the Taylor dispersion method are reported for aqueous solutions of {levodopa (l-dopa) + β-cyclodextrin (β-CD)} solutions at T = 298.15 K and concentrations up to 0.007 mol · dm⁻³. Significant effects on the diffusion were observed, suggesting interactions between this carbohydrate and l-dopa. Support for this came from ¹H NMR spectroscopy, which shows that these effects are due to formation of 1:1 (β-CD:l-dopa) complexes.     

Bound state solutions of D‐dimensional schrödinger equation with exponential‐type potentials

In this article, using an exactly‐solvable multiparameter exponential‐type potential we propose a unified treatment of the analytical bound—state solutions of the Schrödinger equation for exponential‐type potentials in D‐dimensions. Our proposal accepts different approximations to the centrifugal term; however, its usefulness is exemplified in the frame of the Green and Aldrich approach. This fact enables us to compare our results with specific potentials found in the literature and that are obtained here as particular cases of our proposal. That is, instead of solving a specific exponential‐type potential, by resorting each time to a specialized method, the energy spectra and wavefunctions are derived straightforward from the proposed approach. Furthermore, our proposal can be used as an alternative way in the search of solutions to new exponential‐type potentials besides that one can study different approximations to the term . © 2014 Wiley Periodicals, Inc.     

Ideal and non-ideal behaviour of {1-butyl-1-methylpyrrolydinium bis(trifluoromethylsulfonyl)imide + γ-butyrolactone} binary mixtures

Density, electrical conductivity and viscosity of binary liquid mixtures of 1-butyl-1-methylpyrrolydinium bis(trifluoromethylsulfonyl)imide, [bmpyrr][NTf₂], with γ-butyrolactone (GBL) were measured at temperatures from (293.15 to 323.15) K and at atmospheric pressure over the whole composition range. Excess molar volumes have been calculated from the experimental densities and fitted with the Redlich–Kister polynomial equation. These values are positive over the whole range of ionic liquid mole fraction and at all temperatures. In the range between 0.55 and 0.6 [bmpyrr][NTf₂] mole fraction, an ideal behaviour of the ionic liquid mixture with molecular solvent was observed for the first time. Other volumetric properties, such as isobaric thermal expansion coefficients, partial molar volumes and partial molar volumes at infinite dilution have been also calculated, in order to obtain information about interactions between GBL and selected ionic liquid. Positive values of these properties for both components also indicate weaker interactions between GBL and IL compared to the pure components. From the viscosity results, the Angell strength parameter was calculated and found to be 3.24 indicating that [bmpyrr][NTf₂] is a “fragile” liquid. From the volumetric and transport properties obtained, formation of the [bmpyrr]⁺ micellar structures was also discussed. All the results are compared to those obtained for imidazolium-based ionic liquid with GBL.     

Polymer contribution to the thermal conductivity and viscosity in a dilute solution (Fraenkel Dumbbell model)

The phase-space kinetic theory for polymeric liquid mixtures is used to obtain an expression for the polymer contribution to the thermal conductivity of a nonflowing, dilute solution of polymers, where the polymer molecules are modeled as Fraenkel dumbbells. This theory takes into account three mechanisms for the energy transport: diffusion of kinetic energy (including the Öttinger-Petrillo term), diffusion of intramolecular energy, and the work done against the intramolecular forces. This paper is an extension of previous developments for the Hookean dumbbell model and the finitely-extensible dumbbell model. A comparison among the dumbbell results suggests that the thermal conductivity increases with chain stiffness. In addition, the zero-shear-rate viscosity and first normal-stress coefficient are also given for the Fraenkel dumbbell model.Dedicated to Prof. John D. Ferry on the occasion of his 85th birthday.     

Experimental analysis of the steady-state behaviour of beam systems with discontinuous support

This paper deals with the experimental analysis of the long-term behaviour of periodically excited linear beams supported by a one-sided spring or an elastic stop. Numerical analysis of the beams showed subharmonic, quasi-periodic and chaotic behaviour. Furthermore, in the beam system with the one-sided spring three different routes leading to chaos were found. Because of the relative simplicity of the beam systems and the variety of calculated nonlinear phenomena, experimental setups are made of the beam systems to verify the numerical results. The experimental results correspond very well with the numerical results as far as the subharmonic behaviour is concerned. Measured chaotic behaviour is proved to be chaotic by calculating Lyapunov exponents of experimental data.

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Sommario Il presente lavoro concerne l'analisi sperimentale del comportamento a regime di travi lineari, su supporti elastici nonlineari discontinui, eccitate periodicamente. L'analisi numerica dei sistemi in esame ha evidenziato risposte subarmoniche, quasi-periodiche e caotiche, nonchè l'esistenza, nel caso di trave con una molla laterale, di tre differenti percorsi verso il caos. La relativa semplicità dei sistemi di travi ha consentito di procedere ad una verifica sperimentale dei risultati numerici e della varietà dei fenomeni nonlineari da essi evidenziati. La corrispondenza fra risultati sperimentali e numerici è molto buona nel caso di risposta subarmonica. Il comportamento caotico sperimentale è stato convalidato attraverso il calcolo degli esponenti di Lyapunov a partire dai relativi dati.

     

Nonlinear interactions and chaotic dynamics of suspended cables with three-to-one internal resonances

Nonlinear planar oscillations of suspended cables subjected to external excitations with three-to-one internal resonances are investigated. At first, the Galerkin method is used to discretize the governing nonlinear integral–partial-differential equation. Then, the method of multiple scales is applied to obtain the modulation equations in the case of primary resonance. The equilibrium solutions, the periodic solutions and chaotic solutions of the modulation equations are also investigated. The Newton–Raphson method and the pseudo-arclength path-following algorithm are used to obtain the frequency/force–response curves. The supercritical Hopf bifurcations are found in these curves. Choosing these bifurcations as the initial points and applying the shooting method and the pseudo-arclength path-following algorithm, the periodic solution branches are obtained. At the same time, the Floquet theory is used to determine the stability of the periodic solutions. Numerical simulations are used to illustrate the cascades of period-doubling bifurcations leading to chaos. At last, the nonlinear responses of the two-degree-of-freedom model are investigated.