Heat Conduction in One-Dimensional chain of Hard Discs with Substrate Potential

Heat conduction of one-dimensional chain of equivalent rigid particles in the field of external on-site potential is considered. Zero diameters of the particles correspond to exactly integrable case with divergent heat conduction coefficient. By means of simple analytical model it is demonstrated that for any nonzero particle size the integrability is violated and the heat conduction coefficient converges. The result of the analytical computation is verified by means of numerical simulation in a plausible diapason of parameters and good agreement is observedComment: 14 pages, 7 figure

Astrophysical fluid simulations of thermally ideal gases with non-constant adiabatic index: numerical implementation

An Equation of State (\textit{EoS}) closes the set of fluid equations. Although an ideal EoS with a constant \textit{adiabatic index} $\Gamma$ is the preferred choice due to its simplistic implementation, many astrophysical fluid simulations may benefit from a more sophisticated treatment that can account for diverse chemical processes. Here, we first review the basic thermodynamic principles of a gas mixture in terms of its thermal and caloric EoS by including effects like ionization, dissociation as well as temperature dependent degrees of freedom such as molecular vibrations and rotations. The formulation is revisited in the context of plasmas that are either in equilibrium conditions (local thermodynamic- or collisional excitation- equilibria) or described by non-equilibrium chemistry coupled to optically thin radiative cooling. We then present a numerical implementation of thermally ideal gases obeying a more general caloric EoS with non-constant adiabatic index in Godunov-type numerical schemes.We discuss the necessary modifications to the Riemann solver and to the conversion between total energy and pressure (or vice-versa) routinely invoked in Godunov-type schemes. We then present two different approaches for computing the EoS.The first one employs root-finder methods and it is best suited for EoS in analytical form. The second one leans on lookup table and interpolation and results in a more computationally efficient approach although care must be taken to ensure thermodynamic consistency. A number of selected benchmarks demonstrate that the employment of a non-ideal EoS can lead to important differences in the solution when the temperature range is $500-10^4$ K where dissociation and ionization occur. The implementation of selected EoS introduces additional computational costs although using lookup table methods can significantly reduce the overhead by a factor $3\sim 4$.Comment: 17 pages, 10 figures, Accepted for publication in A&

Vibrational and Structural Characterisation in Two Perovskite Challenges: A Density Functional Theory Study

The modelling of perovskites using density functional theory (DFT) can sometimes be a challenge with many different states very close in energy. In particular, the tilting of the inscribed octahedron, as well as the formation of electron polarons, leads to states with energy differences in the meV range. To distinguish between these states requires special care. This thesis investigates how the vibrational frequencies and defect-induced strain, or chemical expansion, can be used to distinguish between different states. For the polaron state in oxyhydride BaTiO3, the comparison of calculations of hydrogen-ion vibrational frequencies to neutron scattering experiments is an excellent discriminator. The presence of polarons is deemed highly unlikely in unstrained material, despite the presence of oxygen vacancies. The observation is confirmed by comparisons of the strain tensor, calculated using a here-developed formalism. In BaZrO3 the likelihood of an anti-ferrodistortive phase transition is a direct consequence of the magnitude of the R25-mode frequency. The R25-mode frequency is strongly dependent on the lattice spacing, but it is shown that the main effect of the inclusion of gradient corrections, as well as non-local correlation, is secondary and is mostly a consequence of the adjusted lattice constant. The inclusion of Fock exchange, however, leads to a significant stabilisation of the cubic phase, which is also verified by neutron scattering measurements. This thesis also concludes that the inclusion of Fock exchange, as found in hybrid functionals, is essential for a correct description of vibrational properties in both two studied perovskites

Micro-macro transitions by interpolation, smoothing, averaging and scaling of particle trajectories

We consider a Newtonian system of many diatomicmolecules each of which consisting of two atoms of equal mass whichare separated by a fixed distance. The barycenters are allowed to movealong some fixed straight line. Moreover each molecule has an additionalrotational degree of freedom. The atoms of neighbouring moleculesinteract to each other by a generic pair potential. By means of thisexample we propose a new method for deriving macroscopic models from microscopic ones. The method is based on the definition of macroscopicobservables and the derivation of corresponding balance laws by interpolation smoothing/averaging and subsequent scaling of particle trajectories