On the Exact Solutions of the Thomas Equation by Algebraic Methods

The Thomas equation is studied to obtain new exact solutions. The wave transformation technique is applied to simplify the main form of the Thomas equation from partial differential equation (PDE) to an ordinary differential equation (ODE). The modified tanh and ($$G'/G$$)-expansion methods are used with the aid of Maple software to arrive at exact solutions for the Thomas equation. Many types of solutions are obtained.

Temperature Effect on the Surface Properties of ZnO(am)

The point of zero charge and surface acidity constants of zinc oxide were determined over the temperature range 293–323 K. Both the point of zero charge (pzc) and the surface acidity constants (pKa1 and pKa2) were found to decrease with increasing temperature. The values of the dissociation constants (pKa1 and pKa2) determined from the Henderson-Hasselbach equation agreed very well with those determined using the Gaines-Thomas equation. The thermodynamic parameters ΔH0 and ΔS0 for the processes were also evaluated.

RELATIVISTIC IONIZATION BY COMPRESSION OF ATOMS AND IONS: A PROPEDEUTICAL STUDY FOR DEGENERATE STELLAR STRUCTURES

Following the relativistic generalization of the Fermi-Thomas equation proposed by Ferrerinho et al.1 we reconsider the Feynmann-Metropolis-Teller treatment2 for compressed atoms and ions. Explicit examples and numerical results are given for the Fermi energies and momenta for selected values of the compression; the ionization by compression curve is given as well. It is remarkable that, even in the most compressed and relativistic configurations, the enhancement of the electron density around the nucleus can never be neglected, so that the electron densities are always far from uniform. Derivation of the electronic distributions for selected values of the compression are given.

Reinforcement Mechanisms in Carbon Black and Silica Loaded Rubber Melts at Low Stresses

For a range of different fillers, silicas and carbon blacks, added to a rubber melt at various concentrations, dynamic moduli in the linear viscoelastic limit have been determined. It is shown that reinforcement is due to hydrodynamic effects and the formation of a secondary particulate structure within the rubber matrix. Both mechanisms can be distinguished experimentally by a frequency sweep. Hydrodynamic reinforcement depends on the filler volume to which immobilized polymer must be added. Its concentration dependence is well described by the semiempirical exponential Thomas Equation. Nominal and effective filler loadings are related by concentration-independent effectiveness factors which can be modelled for all types of fillers considering an immobilized layer of constant height around an agglomerated cluster of filler particles. This provides an explanation for the well-known dependence of reinforcement ability on surface area at small stresses. The chemical and microscopic structure of the filler surface appears to be less important with respect to immobilization ability in the linear viscoelasic regime. The secondary structure formed by the particles is found to be tied together by the elastomer. Its modulus correlates with the filler's immobilization ability and shows little dependence on the filler nature. Due to formation of a filler-polymer structure with individual relaxation times, a strict separability of hydrodynamic and interparticular-reinforcement mechanisms at very high loadings no longer applies.