How to Mix Molecules with Mathematics

In this paper we develop two methods to calculate thermodynamic properties of mixtures. Starting point are the basic assumptions that also form the basis for the COSMO-RS model. In this approach, the individual molecules are represented by their geometrical shape with an electrical charge density on their surfaces. Next, the surface is split up into surface segments each with its own charge. In COSMO-RS a strong reduction is introduced by treating the segments as if they are completely independent. In the present study we take into account that the coupling between two patches is essentially dependent on the charge distribution on neighboring segments and on the local geometrical structure of the surface. Two approaches are followed. The first one points out how the model equations, which comprise the optimization of the entropy and conservation of internal energy, can efficiently be solved in general, thus also if the dependency between segments and the local geometry is included in the expression for the coupling energy between segments. In the second method the configuration with maximal entropy and prescribed energy is sought via simulation. Successive molecular configurations of the mixture are simulated and updated via a genetic algorithm to optimize the entropy. The second method is more time consuming but very general

Experimental realization of SQUIDs with topological insulator junctions

We demonstrate topological insulator (Bi$_2$Te$_3$) dc SQUIDs, based on superconducting Nb leads coupled to nano-fabricated Nb-Bi$_2$Te$_3$-Nb Josephson junctions. The high reproducibility and controllability of the fabrication process allows the creation of dc SQUIDs with parameters that are in agreement with design values. Clear critical current modulation of both the junctions and the SQUID with applied magnetic fields have been observed. We show that the SQUIDs have a periodicity in the voltage-flux characteristic of $\Phi_0$, of relevance to the ongoing pursuit of realizing interferometers for the detection of Majorana fermions in superconductor- topological insulator structures