Dynamical behavior of a stochastic Nicholson’s blowflies model with distributed delay and degenerate diffusion

Nonlinear Dynamics - The mathematical model with time delay is often more practical because it is subject to current and past state. What remains unclear are the details, such as how time delay and...     

On the hyperchaotic complex Lü system

The aim of this paper is to introduce the new hyperchaotic complex Lü system. This system has complex nonlinear behavior which is studied and investigated in this work. Numerically the range of parameter values of the system at which hyperchaotic attractors exist is calculated. This new system has a whole circle of equilibria and three isolated fixed points, while the real counterpart has only three isolated ones. The stability analysis of the trivial fixed point is studied. Its dynamics is more rich in the sense that our system exhibits both chaotic and hyperchaotic attractors, as well as periodic and quasi-periodic solutions and solutions that approach fixed points. The nonlinear control method based on Lyapunov function is used to synchronize the hyperchaotic attractors. The control of these attractors is studied. Different forms of hyperchaotic complex Lü systems are constructed using the state feedback controller and complex periodic forcing.     

Absolute nodal coordinate formulation of large-deformation piezoelectric laminated plates

The Absolute Nodal Coordinate Formulation (ANCF) has been initiated in 1996 by Shabana (Computational Continuum Mechanics, 3rd edn., Cambridge: Cambridge University Press, 2008). It introduces large displacements of planar and spatial finite elements relative to the global reference frame without using any local frame. A sub-family of beam, plate and cable finite elements with large deformations are proposed and employed the 3D theory of continuum mechanics. In the ANCF, the nodal coordinates consist of absolute position coordinates and gradients that can be used to define a unique rotation and deformation fields within the element. In contrast to other large deformation formulations, the equations of motion contain constant mass matrices as well as zero centrifugal and Coriolis inertia forces. The only nonlinear term is a vector of elastic forces. This investigation concerns a way to generate new finite element in the ANCF for laminated composite plates. This formulation utilizes the assumption that the bonds between the laminae are thin and shear is non-deformable. Consequently, the Equivalent Single Layer, ESL model, is implemented. In the ESL models, the laminate is assumed to deform as a single layer, assuming a smooth variation of the displacement field across the thickness. In this paper, the coupled electromechanical effect of Piezoelectric Laminated Plate is imposed within the ANCF thin plate element, in such a way as to achieve the continuity of the gradients at the nodal points, and obtain a formulation that automatically satisfies the principle of work and energy. Convergence and accuracy of the finite-element ANCF Piezoelectric Laminated Plate is demonstrated in geometrically nonlinear static and dynamic test problems, as well as in linear analysis of natural frequencies. The computer implementation and several numerical examples are presented in order to demonstrate the use of the formulation developed in this paper. A comparison with the commercial finite element package COMSOL MULTIPHYSICS () is carried out with an excellent agreement.     

Fractional order theory in thermoelastic solid with three-phase lag heat transfer

In this work, the field equations of the linear theory of thermoelasticity have been constructed in the context of a new consideration of Fourier law of heat conduction with time-fractional order and three-phase lag. A uniqueness and reciprocity theorems are proved. One-dimensional application for a half-space of elastic material in the presence of heat sources has been solved using Laplace transform and state space techniques Ezzat (Canad J Phys Rev 86:1241–1250, 2008). According to the numerical results and its graphs, conclusion about the new theory has been established.     

Chemically reactive and radiative von Kármán swirling flow due to a rotating disk

A new mathematical model is presented to study the heat and mass transfer characteristics of magnetohydrodynamic (MHD) Maxwell fluid flow over a convectively heated stretchable rotating disk. To regulate the fluid temperature at the surface, a simple isothermal model of homogeneous-heterogeneous reactions is employed. The impact of nonlinear thermal radiative heat flux on thermal transport features is studied. The transformed nonlinear system of ordinary differential equations is solved numerically with an efficient method, namely, the Runge-Kutta-Felberg fourth-order and fifth-order (RKF45) integration scheme using the MAPLE software. Achieved results are validated with previous studies in an excellent way. Major outcomes reveal that the magnetic flux reduces the velocity components in the radial, angular, and axial directions, and enhances the fluid temperature. Also, the presence of radiative heat flux is to raise the temperature of fluid. Further, the strength of homogeneous–heterogeneous reactions is useful to diminish the concentration of reaction.     

On the Use of the Restitution Condition in Flexible Body Dynamics

The difference between the classical treatment offlexible body impact and the treatment of impact in flexiblemultibody dynamics is due to several fundamental reasons. Inthe classical impact theory, simple structures such as beamsand plates are used. Infinite dimensional models can bedeveloped for these simple structural elements to study theimpact dynamics and the wave propagation problem. Flexiblemultibody impact problems, on the other hand, involve bodieswith complex geometry that cannot be modeled using infinitenumber of degrees of freedom. Furthermore, the classicalimpact theory has been mainly concerned with the impactbetween a rigid mass that moves without constraints beforeit impacts a simple flexible structure. This is not amultibody simulation scenario in which the impact occursbetween kinematically constrained bodies that are subjectedto impulsive constraint forces in addition to the impactforces. These constraint forces can influence the motion ofthe two bodies immediately after impact, and as aconsequence, the simple classical theory scenario of impactdoes not apply. It is the objective of this paper to discussthe use of the restitution condition in flexible multibodyimpact problems and demonstrate that the use of thisapproach does not exclude the classical formulation.Nonetheless, the impulse momentum balance approach can serveas an effective and efficient procedure for solving theimpact problem in finite dimensional models that do not obeythe classical wave theory. Energy results of simplestructural elements are presented in order to demonstratethe consistency of using the impulse momentum balanceapproach in solving impact problems in finite dimensionalflexible body applications.     

Linear viscoelastic properties of emulsions and suspensions with thermodynamic and hydrodynamic interactions

We present a new approach to describe the rheological properties of dispersions with non-hydrodynamic interactions (steric, electrostatic and Van der Waals interactions) in the linear viscoelastic domain. Our model is based on the calculation of additional stresses resulting from interaction potentials between spheres and Brownian motion. We start from the statistical mechanical approaches which have been developed by Batchelor and Green and later Lionberger and Russel, to model the viscoelastic properties of emulsions and suspensions. We have extended their calculations to the more general case of viscoelastic deformable inclusions in a viscoelastic matrix. Our contribution lies in the computation of the hydrodynamic functions involved in the term describing interaction stresses. This computation is based on Palierne's results on the deformation field around a viscoelastic inclusion embedded in a viscoelastic matrix. We have also rewritten the conservation equation in the case of interest, over the whole frequency domain. We finally express the complex shear modulus of the dispersion as the sum of two terms : Palierne's complex shear modulus gives the purely hydrodynamic contribution; the interaction contribution depends on both the hydrodynamic properties and the interaction potential.     

Absorption spectra of 2-styryl-4-phenyl-thiazole ethiodides in organic solvents of varying polarities and determination of the formation constant of the charge transfer complex formed

The electronic absorption spectra of some 2-styryl-4-phenyl-thiazole ethiodides are studied in organic solvents of different polarities. The shorter wavelength band appearing in the visible region is assigned to an intramolecular charge transfer (CT)-transition originating from the phenyl moiety to the positively charged hetero ring, while the longer wavelength one is due to an intermolecular CT-transition from the iodide ion to the 2-styryl-4-phenyl-thiazolinium cation. These assignments are based on the nature of the aldehydic residue and effects of solvent, concentration, and temperature on both the position and absorptivity of the CT complex-band. It is concluded that the CT complex formed will be highly solvated inDMF, DMSO, ethanol and methanol relative to in CHCl₃, dioxane and acetone. The formation constant of the CT complex in solutions of different polarities is determined at different temperatures. Furthermore, the thermodynamic parameters H ^o, G ^o and S ^o for complex formation are calculated and discussed.

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Absorptionsspektren von 2-Styryl-4-phenyl-thiazol-ethiodiden in verschiedenen Lösungsmitteln und Bestimmung der Bildungskonstanten der Charge-Transfer-Komplexe

Zusammenfassung Die Elektronenanregungsspektren einiger substituierter 2-Styryl-4-phenyl-thiazol-ethiodide wurden in einigen Lösungsmitteln unterschiedlicher Polarität untersucht. Die Absorption bei kürzerer Wellenlänge wird einem intramolekularen Charge-Transfer (CT)-Übergang zugeordnet, die langwellige Bande einem intermolekularen CT-Übergang (Jodid—organ. Kation). Die Diskussion erfolgt basierend auf Substitutions-, Lösungsmittel-, Konzentrations-, und Temperatur-Effekten. Die Komplexbildungskonstanten und die thermodynamischen Parameter H ^o, G ^o und S ^o werden angegeben.

     

Crystal and molecular structure of triphenylarsine

Triphenylarsine crystallizes in the triclinic space groupP¯1 (No. 2),a=11.200(2),b=15.263(7),c=17.871(6) Å,=84.63(5),=80.21(5), =86.41(6)°,Z=8, with four molecules in the asymmetric unit. The structure was solved by direct methods and refined in the initial stages by full-matrix least squares and finally by block-diagonal least-squares methods toR=0.055 for 3537 reflections. The dimensions and the conformations of the four independent molecules are almost identical. The molecules do not exhibitC _3v symmetry.