Accurate simulation estimates of phase behaviour in ternary mixtures with prescribed composition

This paper describes an isobaric semi-grand canonical ensemble Monte Carlo scheme for the accurate study of phase behaviour in ternary fluid mixtures under the experimentally relevant conditions of prescribed pressure, temperature and overall composition. It is shown how to tune the relative chemical potentials of the individual components to target some requisite overall composition and how, in regions of phase coexistence, to extract accurate estimates for the compositions and phase fractions of individual coexisting phases. The method is illustrated by tracking a path through the composition space of a model ternary Lennard-Jones mixture.Comment: 6 pages, 3 figure

Continuous demixing at liquid-vapor coexistence in a symmetrical binary fluid mixture

We report a Monte Carlo finite-size scaling study of the demixing transition of a symmetrical Lennard-Jones binary fluid mixture. For equal concentration of species, and for a choice of the unlike-to-like interaction ratio delta=0.7, this transition is found to be continuous at liquid-vapor coexistence. The associated critical end point exhibits Ising-like universality. These findings confirm those of earlier smaller scale simulation studies of the same model, but contradict the findings of recent integral equation and hierarchical reference theory investigations.Comment: 7 pages, 6 figure

Lattice-switch Monte Carlo

We present a Monte Carlo method for the direct evaluation of the difference between the free energies of two crystal structures. The method is built on a lattice-switch transformation that maps a configuration of one structure onto a candidate configuration of the other by `switching' one set of lattice vectors for the other, while keeping the displacements with respect to the lattice sites constant. The sampling of the displacement configurations is biased, multicanonically, to favor paths leading to `gateway' arrangements for which the Monte Carlo switch to the candidate configuration will be accepted. The configurations of both structures can then be efficiently sampled in a single process, and the difference between their free energies evaluated from their measured probabilities. We explore and exploit the method in the context of extensive studies of systems of hard spheres. We show that the efficiency of the method is controlled by the extent to which the switch conserves correlated microstructure. We also show how, microscopically, the procedure works: the system finds gateway arrangements which fulfill the sampling bias intelligently. We establish, with high precision, the differences between the free energies of the two close packed structures (fcc and hcp) in both the constant density and the constant pressure ensembles.Comment: 34 pages, 9 figures, RevTeX. To appear in Phys. Rev.

Critical end point behaviour in a binary fluid mixture

We consider the liquid-gas phase boundary in a binary fluid mixture near its critical end point. Using general scaling arguments we show that the diameter of the liquid-gas coexistence curve exhibits singular behaviour as the critical end point is approached. This prediction is tested by means of extensive Monte-Carlo simulations of a symmetrical Lennard-Jones binary mixture within the grand canonical ensemble. The simulation results show clear evidence for the proposed singularity, as well as confirming a previously predicted singularity in the coexistence chemical potential [Fisher and Upton, Phys. Rev. Lett. 65, 2402 (1990)]. The results suggest that the observed singularities, particularly that in the coexistence diameter, should also be detectable experimentally.Comment: 17 pages Revtex, 11 epsf figures. To appear in Phys. Rev.

On the Potts model partition function in an external field

We study the partition function of Potts model in an external (magnetic) field, and its connections with the zero-field Potts model partition function. Using a deletion-contraction formulation for the partition function Z for this model, we show that it can be expanded in terms of the zero-field partition function. We also show that Z can be written as a sum over the spanning trees, and the spanning forests, of a graph G. Our results extend to Z the well-known spanning tree expansion for the zero-field partition function that arises though its connections with the Tutte polynomial

On twisted Fourier analysis and convergence of Fourier series on discrete groups

We study norm convergence and summability of Fourier series in the setting of reduced twisted group $C^*$-algebras of discrete groups. For amenable groups, F{\o}lner nets give the key to Fej\'er summation. We show that Abel-Poisson summation holds for a large class of groups, including e.g. all Coxeter groups and all Gromov hyperbolic groups. As a tool in our presentation, we introduce notions of polynomial and subexponential H-growth for countable groups w.r.t. proper scale functions, usually chosen as length functions. These coincide with the classical notions of growth in the case of amenable groups.Comment: 35 pages; abridged, revised and update

Clinical and Pathological Phenotypes of LRP10 Variant Carriers with Dementia

BACKGROUND: Rare variants in the low-density lipoprotein receptor related protein 10 gene (LRP10) have recently been implicated in the etiology of Parkinson's disease (PD) and dementia with Lewy bodies (DLB). OBJECTIVE: We searched for LRP10 variants in a new series of brain donors with dementia and Lewy pathology (LP) at autopsy, or dementia and parkinsonism without LP but with various other neurodegenerative pathologies. METHODS: Sanger sequencing of LRP10 was performed in 233 donors collected by the Netherlands Brain Bank. RESULTS: Rare, possibly pathogenic heterozygous LRP10 variants were present in three patients: p.Gly453Ser in a patient with mixed Alzheimer's disease (AD)/Lewy body disease (LBD), p.Arg151Cys in a DLB patient, and p.Gly326Asp in an AD patient without LP. All three patients had a positive family history for dementia or PD. CONCLUSION: Rare LRP10 variants are present in some patients with dementia and different brain pathologies including DLB, mixed AD/LBD, and AD. These findings suggest a role for LRP10 across a broad neurodegenerative spectrum

Scaling and universality in the phase diagram of the 2D Blume-Capel model

We review the pertinent features of the phase diagram of the zero-field Blume-Capel model, focusing on the aspects of transition order, finite-size scaling and universality. In particular, we employ a range of Monte Carlo simulation methods to study the 2D spin-1 Blume-Capel model on the square lattice to investigate the behavior in the vicinity of the first-order and second-order regimes of the ferromagnet-paramagnet phase boundary, respectively. To achieve high-precision results, we utilize a combination of (i) a parallel version of the multicanonical algorithm and (ii) a hybrid updating scheme combining Metropolis and generalized Wolff cluster moves. These techniques are combined to study for the first time the correlation length of the model, using its scaling in the regime of second-order transitions to illustrate universality through the observed identity of the limiting value of $\xi/L$ with the exactly known result for the Ising universality class.Comment: 16 pages, 7 figures, 1 table, submitted to Eur. Phys. J. Special Topic

Quantum walks: a comprehensive review

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists, mathematicians and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing Journa