Random cluster model on a Cayley tree

The random cluster model of Kasteleyn and Fortuin, which comprises the Ashkin-Teller-Potts model, the Ising model and the bond percolation problem, is solved on a Cayley tree. The solution is discussed both on a whole tree including the surface and in the interior of a tree. Emphasis is put on including several external fields into the model. Phase transitions and phase diagrams are investigated extensively.     

Self-pulsing at stimulated scattering processes

Periodic pulsations of the output intensity at stimulated scattering processes are shown to occur in the presence of a feedback of the scattered wave, produced by partial reflection at the edges of the scattering medium. The scaling of the oscillation period is given for both forward and back scattering.     

Rates of homogeneous ice nucleation in levitated H2O and D2O droplets

Rates of homogeneous nucleation of H2O droplets in a temperature range from 236.37 to 237.91 K and of D2O droplets from 241.34 to 242.33 K were measured. The single microdroplets consisted of pure H2O or D2O and were levitated in an electrodynamic balance. In comparison to H2O, D2O shows a stronger tendency to nucleate. Over the investigated temperature interval, D2O droplets need to be supercooled less by 1.1 K compared to H2O droplets in order to arrive at the same nucleation rate. This is in good agreement with the higher degree of intermolecular association in liquid D2O, a fact which has been well established previously both from theory and experimental studies.     

Relaxation and thermal vibrations at the NaF(100) surface

The relaxation and the thermal vibrations of the NaF(100) surface are investigated in the temperature range between 25 K and 230 K by means of low-energy electron diffraction (LEED) and a subsequent I(V) structure analysis based on the tensor LEED approach (TLEED). According to the experiments, the NaF(100) surface is not significantly relaxed and has the ideal truncated bulk structure. The thermal vibrational amplitudes of the ions in the topmost layer are significantly enhanced compared to the bulk by a factor of 1.35 ± 0.15 and are equal within the error-bars for Na⁺ and F^? ions. Moreover, the relaxation and the dynamics of the NaF(100) surface are investigated using periodic density functional theory (DFT) calculations using pseudopotentials. In agreement with the experimental findings, the calculated relaxation of the NaF(100) surface is weak with static shifts of the ions of 0.01 Å to 0.02 Å. In the topmost layer, the Na⁺ ions are predicted to be slightly inward shifted, whereas the F^? ions are outward shifted, in accordance to predictions of previous shell-model calculations. A Born Oppenheimer molecular dynamics (BO-MD) simulation of the dynamics at the NaF(100) surface leads to a smaller enhancement of thermal motions of the ions at the surface compared to the experiment.