Order in chaotic pseudoplastic flow between coaxial cylinders

Order is found within the chaotic nonlinear flow between rotating coaxial cylinders. The flow stability analysis is carried out for a pseudoplastic fluid through bifurcation diagram and Lyapunov exponent histogram. The fluid is assumed to follow the Carreau–Bird model, and mixed boundary conditions are imposed. The low-order dynamical system, resulted from Galerkin projection of the conservation of mass and momentum equations, includes additional nonlinear terms in the velocity components originated from the shear-dependent viscosity. It is observed that the base flow loses its radial flow stability to the vortex structure at a lower critical Taylor number, as the shear-thinning effects increase. The emergence of the vortices corresponds to the onset of a supercritical bifurcation, which is also seen in the flow of a linear fluid. However, unlike the Newtonian case, shear-thinning Taylor vortices lose their stability as the Taylor number reaches a second critical number corresponding to the onset of a Hopf bifurcation. Complete flow field together with viscosity maps are given for different scenarios in the bifurcation diagram.     

A pseudo‐viscoelastic approach for transient polymeric flow exiting a channel

The influence of elasticity of a fluid exiting a channel is examined on transient coating downstream. A hybrid spectral/boundary element approach is proposed to solve the problem. The flow inside the channel is assumed to be fully developed. A viscoelastic instability of one‐dimensional plane Couette flow is first determined for a large class of Oldroyd fluids with added viscosity, which typically represent polymer solutions composed of a Newtonian solvent and a polymeric solute. The Johnson–Segalman equation is used as the constitutive model. The velocity profile inside the channel is taken as the exit profile for the emerging free‐surface flow. The flow is assumed to be Newtonian as it emerges from the channel. An estimate of the magnitude of the rate‐of‐strain tensor components in the free‐surface region reveals that they are generally smaller than the shear rate inside the channel. The evolution of the flow front is simulated using the boundary element method. For the channel flow, the problem is reduced to a nonlinear dynamical system using the Galerkin projection method. Stability analysis indicates that the channel velocity may be linear or non‐linear depending on the range of the Weissenberg number. The evolution of the coating flow at the exit is examined for steady as well as transient (monotonic and oscillatory) channel flow. It is found that adverse flow can exist as a result of fluid elasticity, which can hinder the process of blade coating. Copyright © 2003 John Wiley & Sons, Ltd.     

Laguerre Wavelet Approach for a Two-Dimensional Time–Space Fractional Schrödinger Equation

This article is devoted to the determination of numerical solutions for the two-dimensional time–spacefractional Schrödinger equation. To do this, the unknown parameters are obtained using the Laguerre wavelet approach. We discretize the problem by using this technique. Then, we solve the discretized nonlinear problem by means of a collocation method. The method was proven to give very accurate results. The given numerical examples support this claim.     

Generating pairs for the held groupHe

A groupG is said to be (l, m, n)-generated if it is a quotient group of the triangle groupT(p,q,r)=<x,y,z?x ^p =y ^q =z ^r =xyz=1>. In [15], the question of finding all triples (l, m, n) such that non-abelian finite simple groups are (l, m, n)-generated was posed. In this paper we partially answer this question for the sporadic groupHe. We continue the study of (p, q, r)-generations of the sporadic simple groups, where,p, q, r are distinct primes. The problem is resolved for the Held groupHe.     

Full non-rigid group theory and symmetry of melamine

The non-rigid molecule group (NRG) theory in which the dynamic symmetry operations are defined as physical operations is a new field in chemistry. Smeyers, in a series of papers, applied this notion to determine the character table of restricted NRG of some molecules. For example, Smeyers and Villa computed the r-NRG of the triple equivalent methyl rotation in pyramidal trimethylamine with inversion and proved that the r-NRG of this molecule is a group of order 648, containing two subgroups of order 324 without inversion [5]. In this work, a simple method is described, through which it is possible to calculate character tables for the symmetry group of molecules. We study the full NRG of melamine, and prove that it is a groups of order 48, with 27 and 10 conjugacy classes. Also, we compute the symmetry of melamine and prove that it is a non-abelian groups of order 6. The method can be generalized to apply to other non-rigid molecules.     

The PI index of product graphs

The Padmakar–Ivan index of a graph G is the sum over all edges uv of G of number of edges which are not equidistant from u and v. In this work, an exact expression for the PI index of the Cartesian product of bipartite graphs is computed. Using this formula, the PI indices of C₄ nanotubes and nanotori are computed.     

Conductance study of the thermodynamics of complexation of amantadine, rimantadine and aminocyclohexane with some macrocyclic compounds in acetonitrile solution

A conductance study concerning the interaction between cationic organic ammonium ions amantadine, rimantadine, and aminocyclohexane with 18-crown-6 (18C6), dicyclohexyl-18-crown-6 (DC18C6) and cryptand C222 in acetonitrile solution has been carried out at different temperatures. The stability constants of the resulting 1:1 cornplexes at various temperatures were determined from the computer fitting of molar conductance-mole ratio data. The enthalpy and entropy of complexation reactions were evaluated from the temperature dependence of the formation constants. The influences of different parameters such as steric hindrance of organic amines and macrocycles, conformations of the free and complexed ligands, and solvent-ligand interaction on the thermodynamic data are discussed.     

Nonrigid group theory for 1,3,5‐trimethylbenzene

Using nonrigid group theory, the full nonrigid (f‐NRG) group of 1,3,5‐trimethylbenzene (TMB) is shown to be isomorphic to the group S₃[C₃] = C₃ S₃ of order 162, where denotes the wreath product of groups, and C₃ is the cyclic group of order three and S₃ is the symmetric group of order six on three letters. This group has 22 conjugacy classes and irreducible representations. The character table of the full nonrigid TMB is then derived for the first time. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007