Jasna Rubčić

Scale-invariant power law and fractality for molecular weights

The fractal ideas of Mandelbrot are extended to the systematics of molecular weights of chemical compounds. A scale-invariant power law for molecular weights is introduced and exemplified for a randomly selected set of molecules and their dependence on effective molecular number. It is also shown that the isotopic composition of chemical compounds is characterized by a fractal pattern, which extends over the range of more than two orders of magnitude.

Power laws and fractal behavior in nuclear stability, atomic weights and molecular weights

Abstract A power law is introduced for the description of the line of stability of atomic nuclei, and for the description of atomic weights and molecular weights. The power law for the line of stability is compared with the semi-empirical formula of the liquid drop model. It is shown that the power law corresponds to a reduction of neutron excess in super-heavy nuclei with respect to the semi-microscopic formula. Some fractal features of the nuclear valley of stability and of the isotopic abundance set of molecules are shown and the corresponding fractal dimensions are determined. With respect to the problem of truncating fractals of natural objects, it is shown that a simple mathematical model of an extended map on an annulus provides a similar type of truncated fractals. It is argued that the origin of the observed fractal property of nuclei, atoms and molecules lies in the basic fractal nature of quantum mechanics.

Modeling the physical properties of a homologous series on the melting temperatures and densities of n-alkanes and their simple alkyl-derivatives

Abstract Several aspects of the melting temperatures (MT) of linear chain homologs are discussed. It is shown that with some reasonable modifications of Einsteins model of simple solids, the MT of n-alkanes and their derivatives can be successfully modeled. Results are compared with those obtained by previous authors who have used numerical methods and thermodynamics. Results of investigation of quadratic recurrence relations of the second order and forms including exponential functions are reported. Finally, the correlation of MT with density at T = 298.15 K gives the limiting value, 0.86 gcm-3 , at the temperature of nearly 420 K. It is expected that proper correlations should use densities of liquids just at the MT, because some available data suggest a linear dependence of MT on density. All results obtained are mutually consistent

Fractality for the Nuclear Line of Stability, Atomic Weights and Molecular Weights

We point out that the N, Z-chart of stable isotopes displays a fractal pattern with fractal dimension d f ≈ 1.2. On this basis a scale invariant power law for the line of beta stability is introduced. For stable nuclei the power law pattern compares well with the semiempirical model, providing even a slightly better fit of data. We argue that the semiempirical description of the line of beta stability is inherently related to the underlying fractality. Extrapolating to the superheavy region, a slightly slower increase of neutron excess with increasing mass number was found for the power law than in the semimicroscopic model. In the same framework we proposed the power laws for the systematics of atomic and molecular weights of chemical elements and compounds.