Simplified Onsager theory for isotropic-nematic phase equilibria of length polydisperse hard rods

Polydispersity is believed to have important effects on the formation of liquid crystal phases in suspensions of rod-like particles. To understand such effects, we analyse the phase behaviour of thin hard rods with length polydispersity. Our treatment is based on a simplified Onsager theory, obtained by truncating the series expansion of the angular dependence of the excluded volume. We describe the model and give the full phase equilibrium equations; these are then solved numerically using the moment free energy method which reduces the problem from one with an infinite number of conserved densities to one with a finite number of effective densities that are moments of the full density distribution. The method yields exactly the onset of nematic ordering. Beyond this, results are approximate but we show that they can be made essentially arbitrarily precise by adding adaptively chosen extra moments, while still avoiding the numerical complications of a direct solution of the full phase equilibrium conditions. We investigate in detail the phase behaviour of systems with three different length distributions: a (unimodal) Schulz distribution, a bidisperse distribution and a bimodal mixture of two Schulz distributions which interpolates between these two cases. A three-phase isotropic-nematic-nematic coexistence region is shown to exist for the bimodal and bidisperse length distributions if the ratio of long and short rod lengths is sufficiently large, but not for the unimodal one. We systematically explore the topology of the phase diagram as a function of the width of the length distribution and of the rod length ratio in the bidisperse and bimodal cases.Comment: 18 pages, 16 figure

Electronic spectra of carbon chains and rings: Astrophysical relevance?

Our research has focused on the measurement of the electronic spectra of unstable molecules which are presumed to be of relevance to astrophysical observations. Among these are the carbon chains and their ions. Thus we have been using and developing a number of spectroscopic methods to determine their spectra in the gas phase, including absorption via cavity ring-down and REMPI methods. The species are produced in supersonic jets coupled with discharge and laser ablation sources. With the successful laboratory detection of the electronic spectra of a number of key species, such as bare carbon chains Cn n=4,5, comparisons with astrophysical data could be made which lead to interesting implications for the future search for the species which could be responsible for the diffuse interstellar bands. Among the recent relevant observations in the laboratory have been the electronic spectra of carbon rings, Cn n=14,18,22, the development of a method to study transitions in mass-selected ions collisionally relaxed to 20 K and held in a 22-pole radiofrequency trap, and the study of metal containing carbon chain

Systematic study of d-wave superconductivity in the 2D repulsive Hubbard model

The cluster size dependence of superconductivity in the conventional two-dimensional Hubbard model, commonly believed to describe high-temperature superconductors, is systematically studied using the Dynamical Cluster Approximation and Quantum Monte Carlo simulations as cluster solver. Due to the non-locality of the d-wave superconducting order parameter, the results on small clusters show large size and geometry effects. In large enough clusters, the results are independent of the cluster size and display a finite temperature instability to d-wave superconductivity.Comment: 4 pages, 3 figures; updated with version published in PRL; added values of Tc obtained from fit

EIT ground-state cooling of long ion strings

Electromagnetically-induced-transparency (EIT) cooling is a ground-state cooling technique for trapped particles. EIT offers a broader cooling range in frequency space compared to more established methods. In this work, we experimentally investigate EIT cooling in strings of trapped atomic ions. In strings of up to 18 ions, we demonstrate simultaneous ground state cooling of all radial modes in under 1 ms. This is a particularly important capability in view of emerging quantum simulation experiments with large numbers of trapped ions. Our analysis of the EIT cooling dynamics is based on a novel technique enabling single-shot measurements of phonon numbers, by rapid adiabatic passage on a vibrational sideband of a narrow transition

Dynamics and Scaling of 2D Polymers in a Dilute Solution

The breakdown of dynamical scaling for a dilute polymer solution in 2D has been suggested by Shannon and Choy [Phys. Rev. Lett. {\bf 79}, 1455 (1997)]. However, we show here both numerically and analytically that dynamical scaling holds when the finite-size dependence of the relevant dynamical quantities is properly taken into account. We carry out large-scale simulations in 2D for a polymer chain in a good solvent with full hydrodynamic interactions to verify dynamical scaling. This is achieved by novel mesoscopic simulation techniques

Probably Safe or Live

This paper presents a formal characterisation of safety and liveness properties \`a la Alpern and Schneider for fully probabilistic systems. As for the classical setting, it is established that any (probabilistic tree) property is equivalent to a conjunction of a safety and liveness property. A simple algorithm is provided to obtain such property decomposition for flat probabilistic CTL (PCTL). A safe fragment of PCTL is identified that provides a sound and complete characterisation of safety properties. For liveness properties, we provide two PCTL fragments, a sound and a complete one. We show that safety properties only have finite counterexamples, whereas liveness properties have none. We compare our characterisation for qualitative properties with the one for branching time properties by Manolios and Trefler, and present sound and complete PCTL fragments for characterising the notions of strong safety and absolute liveness coined by Sistla

Pairing symmetry of the one-band Hubbard model in the paramagnetic weak-coupling limit: a numerical RPA study

We study the spin-fluctuation-mediated superconducting pairing gap in a weak-coupling approach to the Hubbard model for a two dimensional square lattice in the paramagnetic state. Performing a comprehensive theoretical study of the phase diagram as a function of filling, we find that the superconducting gap exhibits transitions from p-wave at very low electron fillings to d_{x^2-y^2}-wave symmetry close to half filling in agreement with previous reports. At intermediate filling levels, different gap symmetries appear as a consequence of the changes in the Fermi surface topology and the associated structure of the spin susceptibility. In particular, the vicinity of a van Hove singularity in the electronic structure close to the Fermi level has important consequences for the gap structure in favoring the otherwise sub-dominant triplet solution over the singlet d-wave solution. By solving the full gap equation, we find that the energetically favorable triplet solutions are chiral and break time reversal symmetry. Finally, we also calculate the detailed angular gap structure of the quasi-particle spectrum, and show how spin-fluctuation-mediated pairing leads to significant deviations from the first harmonics both in the singlet d_{x^2-y^2} gap as well as the chiral triplet gap solution.Comment: 11 pages 11 figure