We report periodic B3LYP6-31G(**) density functional theory calculations on Li-doped polythiophene at various dopant concentrations using (SC(4)H(2))(m)Li(2) unit cells for m=2, 6, and 10. Uniform doping by Li atoms and by pairs of Li atoms on adjacent thiophene rings are considered with the primary aim of comparing polaron versus bipolaron properties. Properties examined include geometries, charge distributions, polaron/bipolaron formation energies, dopant binding energies, band structures, and densities of states.

We report periodic B3LYP/6−31G** density functional theory calculations on Na-doped quasi-one-dimensional trans-polyacetylene (PA) chains at various dopant concentrations. The chains are modeled using C2m H2m Na2 unit cells (m = 11, 13, 21, and 31). Our main purpose is to compare with previous calculations on Li-doping. Properties compared include geometries, atomic charges, dopant binding energies, band structures, densities of states, and nature of binding. In contrast with Li, the Na-doped chains are dissociative at concentrations of Na/C ≥ 1/9, and the bond length alternation is reduced for Na-doping as compared to Li-doping. The most significant differences are the binding energies and the appearance of a narrow isolated unoccupied band within the PA π−π* gap in the case of Na-doping. This intragap band is predominantly composed of Na(3s,3p) atomic orbitals.

In the present work we consider the mathematical model that describes brain tumour growth (glioblastomas) under medical treatment. Based on the medical study presented by R. Stupp et al. (New Engl Journal of Med 352: 987-996, 2005) which evidence that, combined therapies such as, radiotherapy and chemotherapy, produces negative tumour-growth, and using the mathematical model of P. K. Burgess et al. (J Neuropath and Exp Neur 56: 704-713, 1997) as an starting point, we present a model for tumour growth under medical treatment represented by a non-linear partial differential equation that is solved using the Adomian Decomposition Method (ADM). It is also shown that the non-linear term efficiently models the effects of the combined therapies. By means of a proper use of parameters, this model could be used for calculating doses in radiotherapy and chemotherapy.

In this work we present a scalar field theory invariant under spacetime anisotropic transformations with a dynamic exponent z. It is shown that this theory possess symmetries similar to Hořava gravity and that in the limit z = 0 the equations of motion of the nonrelativistic MOND theory are obtained. This result allow us to conjecture the existence of a Hořava type gravity that in the limit z = 0 is consistent with MOND.

The Kompaneets equation is a nonlinear partial differential equation that plays an important role in astrophysics as it describes the spectra of photons in interaction with a rarefied electron gas. In spite of its importance, exact solution to this nonlinear equation are rarely found in literature. In this work, we solve this equation and present a new approach to obtain the solution by means of the combined use of the Adomian decomposition method and the Laplace transform (LADM). Besides, we illustrate our approach solving two examples in which, two initial photon distributions, well known in astrophysics, are given. We compare the behaviour of the solutions obtained with the only exact solutions given in the literature for the non-relativistic case. Our results indicate that LADM is highly accurate and can be considered a very useful and valuable method.