Preparation and characterization of sol–gel derived glasses in the ternary Na2O–Al2O3–P2O5 system

A new sol–gel synthesis route to organic free Na₂O–Al₂O₃–P₂O₅ xerogels was developed. These xerogels contain P₂O₅ up to 67.5 mole % and Al₂O₃ up to 20 mole % and could be melted to homogeneous glasses in air at significantly lower temperatures than those applied using the conventionally melting method. Aluminum isopropoxide dissolved in isopropanol, orthophosphoric acid dissolved in isopropanol and sodium nitrate were used as precursors for Al₂O₃, P₂O₅ and Na₂O respectively. Clear stable alcoholic solutions were prepared in the presence of HNO₃. Addition of HNO₃ in the concentration used, enabled homogeneous mixing of the precursors, controlled over the gelation step and prevented the fast precipitation of the AlPO₄ crystalline phase which breaks down the glass formation ability. The sol–gel route developed was investigated using different analytical tools. Differential thermal analysis (DTA) coupled with thermo-gravimetric (TG) analysis indicated that neither organic residues nor sodium nitrate residues were present in the dried gels after gelation. Fourier transform infrared spectroscopy (FTIR) showed the presence of all characteristic phosphate groups and bonds in the dried gels, especially the P=O and the P–O–P bonds. Solid state ³¹P Magic angle spinning nuclear magnetic resonance (MAS NMR) revealed the formation of Q² chain-like polyphosphates of variable polymerization degrees in the dried gels. Solid state ²⁷Al MAS NMR revealed that octahedrally coordinated Al is the preferred moiety in the dried gels. However, powder X-ray diffraction (XRD) investigation indicated the presence of crystalline Q¹ oligomeric pyrophosphate species in the dried gels. Isotropic chemical shifts belonging to these pyrophosphate species were also recorded in the ³¹P MAS NMR spectra. Characterization of the prepared glasses showed that their properties are in very good agreement with those glasses prepared by the conventionally melting method.     

Performance of Low Earth Orbit Satellite Systems with Coding

The effect of block, convolutional and Turbo coding on the probability of error and the capacity are investigated for CDMA Low Earth Orbit (LEO) Satellite systems. The model employed assumes a contaminated Gaussian traffic model to be more compatible with different population areas. The conventional Gaussian distribution can be considered as a special case.     

Slow motion of a slightly deformed spherical droplet in a microstretch fluid

Microsystem Technologies - The Stokes axisymmetrical microstretch streaming flow problem past a stationary viscous droplet and as well as the related problem of a viscous streaming flow past a...     

Wave propagation study for axi-symmetric 2D problems of a generalized thermo-visco-elastic half space

We consider axi-symmetric 2D problems for a visco-elastic half space. We utilize Laplace and Hankel transforms. Asymptotic expansions are used to study wave propagation in the medium. The temperature, displacement, and stress distributions are computed and represented graphically for a specific problem.     

A problem in generalized magneto-thermoelasticity for an infinitely long annular cylinder

The problem of an infinitely long annular cylinder whose inner and outer surfaces are subjected to known surrounding temperatures and are traction-free is considered in the presence of an axial uniform magnetic field. The problem is in the context of generalized magneto-thermoelasticity theory with one relaxation time. The Laplace transform with respect to time is used. A numerical method based on a Fourier-series expansion is used for the inversion process. Numerical computations for the temperature, displacement and stress distributions as well as for the induced magnetic and electric fields are carried out and represented graphically.     

STATE-SPACE APPROACH TO TWO-DIMENSIONAL GENERALIZED THERMOELASTICITY PROBLEMS

In this work the state-space formulation for two-dimensional problems of generalized thermoelasticity with one relaxation time is introduced. Laplace and Fourier integral transforms are used The resulting formulation is applied to a problem of a thick plate subject to heating that varies exponentially with time on parts of its upper and lower surfaces. The Fourier transforms are inverted analytically. A numerical method is employed for the inversion of the Laplace transforms. Numerical results are given and illustrated graphically for the problem considered.     

THEORY OF GENERALIZED MICROPOLAR THERMOELASTICITY AND AN AXISYMMETRIC HALF-SPACE PROBLEM

ABSTRACT

The general equations of motion and constitutive equations are derived for a general homogeneous anisotropic medium with a microstructure, taking into account the effects of heat and allowing for second sound effects. A uniqueness theorem is also derived. As an illustration of the obtained equations, we solve a problem for a half-space whose boundary is rigidly fixed and subjected to an axisymmetric thermal shock. There are no body forces, body couples, or heat sources affecting the medium. Laplace and Hankel transform techniques are used. Numerical results are obtained and graphically illustrated.     

Fundamental solution for a line source of heat in the fractional order theory of thermoelasticity using the new Caputo definition

Abstract

The new Caputo Fabrizio fractional differential operator is used to investigate a problem in the fractional order theory of thermoelasticity. The problem concerns an infinite elastic space under the effect of a continuous line source of heat. The problem is solved using asymptotic expansions valid for short times. Laplace and Hankel transforms are used to solve the problem. A brief study to the nature of propagation of waves is introduced. Graphical results are presented and discussed.