Some exact solutions for rotating flows of a generalized Burgers’ fluid in cylindrical domains

The velocity field and the adequate shear stress corresponding to the flow of a generalized Burgers’ fluid model, between two infinite co-axial cylinders, are determined by means of Laplace and finite Hankel transforms. The motion is due to the inner cylinder that applies a time dependent torsional shear to the fluid. The solutions that have been obtained, presented in series form in terms of usual Bessel functions J₁( ? ), J₂( ? ), Y₁( ? ) and Y₂( ? ), satisfy all imposed initial and boundary conditions. Moreover, the corresponding solutions for Burgers’, Oldroyd-B, Maxwell, second grade, Newtonian fluids and large-time transient solutions for generalized Burgers’ fluid are also obtained as special cases of the present general solutions. The effect of various parameters on large-time and transient solutions of generalized Burgers’ fluid is also discussed. Furthermore, for small values of the material parameters, λ₂ and λ₄ or λ₁, λ₂, λ₃ and λ₄, the general solutions corresponding to generalized Burgers’ fluids are going to those for Oldroyd-B and Newtonian fluids, respectively. Finally, the influence of the pertinent parameters on the fluid motion, as well as a comparison between models, is shown by graphical illustrations.     

Elastic-plastic contact model for rough surfaces based on plastic asperity concept

A mathematical formulation for the contact of rough surfaces is presented. The derivation of the contact model is facilitated through the definition of plastic asperities that are assumed to be embedded at a critical depth within the actual surface asperities. The surface asperities are assumed to deform elastically whereas the plastic asperities experience only plastic deformation. The deformation of plastic asperities is made to obey the law of conservation of volume. It is believed that the proposed model is advantageous since (a) it provides a more accurate account of elastic-plastic behavior of surfaces in contact and (b) it is applicable to model formulations that involve asperity shoulder-to-shoulder contact. Comparison of numerical results for estimating true contact area and contact force using the proposed model and the earlier methods suggest that the proposed approach provides a more realistic prediction of elastic-plastic contact behavior.     

He-Ne laser-induced improvement in biochemical, physiological, growth and yield characteristics in sunflower (Helianthus annuus L.)

The water-soaked seeds of sunflower were exposed to low power continuous wave He-Ne laser irradiation of energies 0, 100, 300 and 500 mJ to evaluate the effect on various biochemical, physiological, growth and yield parameters of sunflower. The experiments which consisted of four replicates arranged in a completely randomized design (CRD) were carried out under the greenhouse conditions. The physiological attributes like, photosynthetic rate (A), transpiration rate (E), intrinsic CO(2) concentration (C(i) ), stomatal conductance (g(s)), chlorophyll a and b contents, relative membrane permeability and leaf water (ψ(w)), osmotic (ψ(s)) and turgor (ψ(p)) potentials, relative water contents and leaf area increased significantly as compared to control due to He-Ne treatment of seeds. The activities of superoxide dismutase, peroxidase and catalases and contents of total soluble proteins, malondialdehyde, proline and leaf total phenolic also increased due to laser treatment. Significant increase in growth parameters of sunflower like shoot fresh and dry masses, root fresh and dry masses, root and shoot lengths, number of leaves per plant and stem diameter has also been observed. The contents of K, Ca and Mg in shoot and root were also increased and an overall increase of up to 28.12% was observed due to laser treatment.     

Aromatic A-ring analogues of orobanchol, new germination stimulants for seeds of parasitic weeds

Strigolactones are signaling compounds in plants of increasing importance. In this paper the focus is on their activity as germinating agents for seeds of parasitic weeds. The syntheses of aromatic A-ring analogues of the germination stimulant orobanchol have been described. Starting substrate is the ABC unit of the stimulant GR24. Oxidation at the C-4 position gives a 4-oxo derivative which on subsequent reduction produces two C-4 epimeric alcohols, syn and anti in a ratio of 82 : 3. For practical access of the C-4 anti alcohol, the predominant syn epimer is inverted by a Mitsunobu procedure. The anti C-4 alcohol is then coupled with the D-ring in a one-pot two-step process involving a formylation and a reaction with bromobutenolide to give a mixture of the diastereomeric aromatic A-ring analogues of orobanchol. In contrast, the syn C-4 alcohol cannot be coupled directly with the D-ring. Protection of the C-4 syn OH is a prequisite. The best protecting function is the SEM group as deprotection after coupling with the D-ring can then readily be achieved. The structures of these new analogues have been ascertained by X-ray analyses. Both diastereomers of the C-4 syn as well as the C-4 anti orobanchol analogues have been tested as germination agents of seeds of Striga hermonthica and Orobanche ramosa. In addition, the acetates of both epimeric C-4 alcohols have been prepared and tested. Both diastereomers of the 4-oxo derivative have been prepared and bioassayed as well. The bioassays reveal that the diastereomers having the natural relative configuration are most active. The data also suggest that hydrogen bonding is not an important factor in the binding of the stimulant molecules in the receptor.     

Ab initio investigation of the electronic and vibrational properties for the (CaLi)+ ionic molecule

A wide adiabatic study has been performed for numerous electronic states of CaLi⁺ molecular ion. The adiabatic potential energy curves and their spectroscopic constants (R_e, D_e, ω_e and T_e) have been calculated using an ab initio approach including a nonempirical pseudo-potential for the Ca and Li cores with the core polarisation potentials operator through full configuration interaction (FCI). Thereafter, the energies of vibrational levels and their spacing for all these states have been reported. In addition, the electric dipole moment curves have been investigated for the (1-19) Σ, (1-12) Π and (1-8) Δ electric states. Moreover it lets us check the extreme transition dipole moments (TDM). These behaviours of TDM are more accustomed to estimate the radiative lifetimes for all vibrational levels in 2¹Σ⁺ and 3¹Σ⁺ states. Also, the bound-bound and the bound-free contribution have been calculated precisely and by employing a Franck–Condon (FC) approximation.     

BaSnF4 fast ion conductor: Variations versus the method of preparation and anomalous temperature variation of the quadrupole splitting

A new method of preparation of high performance fluoride ion conductor, BaSnF₄, by water leaching of newly discovered barium tin(II) chloride fluorides, has been designed, and the materials have been studied and compared to the solid prepared by the usual dry method. The unit-cell parameters and crystallite dimensions were found to vary with the method of preparation. In addition, the crystallite dimensions were found to be highly anisotropic for the samples obtained by the wet method. The Mössbauer spectrum is made of a large tin(II) quadrupole doublet, and a broad tin(IV) oxide peak due to surface oxidation. The tin(II) spectrum is in agreement with covalently bonded tin(II) having a strongly stereoactive lone pair. An unusually high dependence of the quadrupole splitting at low temperatures was observed (5.8 times larger than for α-SnF₂).     

On the line graph of the complete tripartite graph

It is shown that the line graph of the complete tripartite graphK_n,n,n is characterized by the spectrum of its adjacency matrix.     

Crystal and molecular structure ofpp-diphenyl-p-tetrakis (perfluoromethyl)ethylene glycol phosphinate

The title compound crystallizes in space groupP¯1 (No. 2) witha=8.796(6),b=10.754(3),c=12.271(2) Å,=68.56(2),=67.68(3),=78.87(4)°, andZ=2. The structure was solved by direct methods and refined by full-matrix least squares toR=0.048. In the tetrahedral geometry around phosphorus, the P-O(22) bond of 1.464(2) Å is shorter than expected. The OO hydrogen bond results in dimer formation, and the substituted glycol shows staggered conformation along the C(12)-C(3) vector.