Isotropic-nematic transition in hard-rod fluids: relation between continuous and restricted-orientation models

We explore models of hard-rod fluids with a finite number of allowed orientations, and construct their bulk phase diagrams within Onsager's second virial theory. For a one-component fluid, we show that the discretization of the orientations leads to the existence of an artificial (almost) perfectly aligned nematic phase, which coexists with the (physical) nematic phase if the number of orientations is sufficiently large, or with the isotropic phase if the number of orientations is small. Its appearance correlates with the accuracy of sampling the nematic orientation distribution within its typical opening angle. For a binary mixture this artificial phase also exists, and a much larger number of orientations is required to shift it to such high densities that it does not interfere with the physical part of the phase diagram.Comment: 4 pages, 2 figures, submitted to PR

Dynamics of Collapse of flexible Polyelectrolytes and Polyampholytes

We provide a theory for the dynamics of collapse of strongly charged polyelectrolytes (PEs) and flexible polyampholytes (PAs) using Langevin equation. After the initial stage, in which counterions condense onto PE, the mechanism of approach to the globular state is similar for PE and PA. In both instances, metastable pearl-necklace structures form in characteristic time scale that is proportional to N^{4/5} where N is the number of monomers. The late stage of collapse occurs by merger of clusters with the largest one growing at the expense of smaller ones (Lifshitz- Slyozov mechanism). The time scale for this process T_{COLL} N. Simulations are used to support the proposed collapse mechanism for PA and PE.Comment: 14 pages, 2 figure

Predicting phase equilibria in polydisperse systems

Many materials containing colloids or polymers are polydisperse: They comprise particles with properties (such as particle diameter, charge, or polymer chain length) that depend continuously on one or several parameters. This review focusses on the theoretical prediction of phase equilibria in polydisperse systems; the presence of an effectively infinite number of distinguishable particle species makes this a highly nontrivial task. I first describe qualitatively some of the novel features of polydisperse phase behaviour, and outline a theoretical framework within which they can be explored. Current techniques for predicting polydisperse phase equilibria are then reviewed. I also discuss applications to some simple model systems including homopolymers and random copolymers, spherical colloids and colloid-polymer mixtures, and liquid crystals formed from rod- and plate-like colloidal particles; the results surveyed give an idea of the rich phenomenology of polydisperse phase behaviour. Extensions to the study of polydispersity effects on interfacial behaviour and phase separation kinetics are outlined briefly.Comment: 48 pages, invited topical review for Journal of Physics: Condensed Matter; uses Institute of Physics style file iopart.cls (included

Analysis of Galileo IOV + FOC signals and E5 RTK performance

The current Galileo constellation in April 2017 comprises both in-orbit validation and full operational capability satellites transmitting signals on five frequencies, i.e., E1, E5a, E5b, E5, and E6. We analyze the power, multipath and noise of these signals using the data collected by four short baselines of various lengths and receiver/antenna types in Perth, Australia, as well as the Netherlands. In our analysis, the Galileo signals, except E5, show different relative noise and multipath performance for different receiver/antenna types. The E5 signal, with a weak dependency on the type of receiver/antenna, shows a significantly lower level of multipath and noise with respect to the other signals. Estimations of the E5 code standard deviation based on the data of each of the mentioned baselines gives a value of about 6 cm, which is further reduced to about 1 cm once the data are corrected for multipath. Due to the superior stochastic properties of E5 signal compared to the other Galileo signals, we further analyze the short-baseline real-time kinematic performance of the Galileo standalone E5 observations. Our findings confirm that the Galileo E5 data, if corrected for the multipath effect, can make (almost) instantaneous ambiguity resolution feasible already based on the current constellation