Mathematical simulation of the evaporation in operation area of a bubble evaporator

Simulation of evaporation in operation area of an evaporator is considered. We obtained a formalized model of this process and optimum conditions of an engineering system on the basis on the analysis.     

On the Spectra of Carbon Nano-Structures

An explicit derivation of dispersion relations and spectra for periodic Schrödinger operators on carbon nano-structures (including graphene and all types of single-wall nano-tubes) is provided.     

Rheological properties of polyacrylates used as synthetic road binders

Most adhesives and binders, including bitumen for asphalt mixture production, are presently produced from petrochemicals after the refining of crude oil. The fact that crude oil reserves are a finite resource means that in the future, it may become necessary to produce these materials from alternative and probably renewable sources. Suitable resources of this kind may include polysaccharides, plant oils and proteins. This paper deals with the synthesis of polymer binders from monomers that could, in future, be derived from renewable resources. These binders consist of polyethyl acrylate (PEA) of different molecular weight, polymethyl acrylate (PMA) and polybutyl acrylate (PBA), which were synthesised from ethyl acrylate, methyl acrylate and butyl acrylate, respectively, by atom transfer radical polymerisation. The rheological properties of these binders were determined by means of oscillatory testing using a dynamic shear rheometer and combinations of stress/strain, temperature and frequency sweeps. The results indicate that PEA can be produced to have rheological properties similar to that of ‘soft’ 100/150 penetration grade bitumen, PMA with similar rheological properties to that of ‘hard’ 10/20 penetration grade bitumen, while PBA, due to its highly viscous nature and low dynamic moduli, cannot be used on its own as a binder. The synthetic polymers were found to be thermo-rheologically simple, and the shift factors, used to produce the dynamic moduli master curves, were found to fit an Arrhenius function.     

Thermoelastoplastic deformation of a thick-walled cylinder with a radial crack

The thermoelastoplastic fracture mechanics problem of a thick-walled cylinder subjected to internal pressure and a nonuniform temperature field is solved by the method of elastic solutions combined with the finite-element method. The correctness of the solution is provided by using the Barenblatt crack model, in which the stress and strain fields are regular. The elastoplastic problem of a cracked cylinder subjected to internal pressure and a nonuniform temperature field are solved. The calculation results are compared with available data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 173–183, May–June, 2008.     

Metal complexes of 2-hetarylindandiones-1,3

The chelate and molecular complexes of 2-(2-benzazolyl, perimidyl)-indandiones-1,3 were synthesized for the first time. The structures of the ligands (tautomeric forms) and complex compounds were determined from the X-ray diffraction, ¹H, ¹³C NMR, and IR data and the quantum-chemical calculations (RHF SCF in 6-31 G** basis).     

Axisymmetric frictionless contact of functionally graded materials

The main interest of this study is a new method to solve the axisymmetric frictionless contact problem of functionally graded materials (FGMs). Based on the fact that an arbitrary curve can be approached by a series of continuous but piecewise linear curves, the FGM is divided into a series of sub-layers with shear modulus varying linearly in each sub-layer and continuous at the sub-interfaces. With this model, the axisymmetric frictionless contact problem of a functionally graded coated half-space is investigated. By using the transfer matrix method and Hankel integral transform technique, the problem is reduced to a Cauchy singular integral equation. The contact pressure, contact region and indentation are calculated for various indenters by solving the equations numerically. An erratum to this article can be found at     

Water wave radiation by a sphere submerged in water with an ice-cover

Using the multipoles method, we formulate the problems of radiation (both heave and sway) of water waves by a submerged sphere in deep as well as in uniform finite depth water with an ice-cover, with the ice-cover being modelled as an elastic plate of very small thickness. In each case this leads to an infinite system of linear equations which are solved numerically by standard techniques. The added-mass and damping coefficients for a heaving and swaying sphere are obtained and depicted graphically against the wave number for various values of the radius of the submerged sphere and flexural rigidity of the ice-cover to show the effect of the presence of ice-cover on these quantities. When the flexural rigidity is taken to be zero, the numerical results for the added-mass and damping coefficient for water with a free surface are recovered.