Average Structures of a Single Knotted Ring Polymer

Two types of average structures of a single knotted ring polymer are studied by Brownian dynamics simulations. For a ring polymer with N segments, its structure is represented by a 3N -dimensional conformation vector consisting of the Cartesian coordinates of the segment positions relative to the center of mass of the ring polymer. The average structure is given by the average conformation vector, which is self-consistently defined as the average of the conformation vectors obtained from a simulation each of which is rotated to minimize its distance from the average conformation vector. From each conformation vector sampled in a simulation, 2N conformation vectors are generated by changing the numbering of the segments. Among the 2N conformation vectors, the one closest to the average conformation vector is used for one type of the average structure. The other type of the averages structure uses all the conformation vectors generated from those sampled in a simulation. In thecase of the former average structure, the knotted part of the average structure is delocalized for small N and becomes localized as N is increased. In the case of the latter average structure, the average structure changes from a double loop structure for small N to a single loop structure for large N, which indicates the localization-delocalization transition of the knotted part.Comment: 15 pages, 19 figures, uses jpsj2.cl

Halogen (F, Cl, Br, and I) Devolatilization During Prograde Subduction: Insights From Western Alps Ophiolites

In order to examine the progressive chemical evolution of halogens (F, Cl, Br, I) in altered ocean crust (AOC) during prograde subduction, this study compares bulk and in situ halogen concentrations in mafic samples from three petrogenetically related exhumed terrains in the Western Alps (the Chenaillet ophiolite, the Queyras ophiolites of the Schistes Lustrés, and the Monviso ophiolite). Samples from the Chenaillet ophiolite represent oceanic crust unaffected by metamorphic halogen loss and define a protolith halogen content (122 μg/g F, 29 μg/g Cl, 82 ng/g Br, and 98 ng/g I). Samples from the Queyras ophiolites experienced blueschist facies conditions, undergoing recrystallization and halogen loss (74 μg/g F, 19 μg/g Cl, 70 ng/g Br, and 63 ng/g I). Eclogite facies samples from the Monviso meta-ophiolite exhibit markedly reduced Cl (8 μg/g Cl) and Br (42 ng/g Br) contents relative to samples from Chenaillet and Queyras. Using electron probe microanalysis (EPMA), F and Cl host minerals (e.g., amphibole, chlorite, epidote) are identified and characterized in selected samples, showing a broad distribution of F and Cl, lending support to the view that halogen devolatilization in the subducting slab occurs continuously and is not dependent on the breakdown of a particular phase. In situ Cl concentrations decrease significantly between sub-greenschist and blueschist assemblages. Fluorine is retained within subducting AOC and is decoupled from the heavy halogens (Cl, Br, I), which undergo continuous devolatilization during prograde metamorphism

Steady-state hydrodynamic instabilities of active liquid crystals: Hybrid lattice Boltzmann simulations

We report hybrid lattice Boltzmann (HLB) simulations of the hydrodynamics of an active nematic liquid crystal sandwiched between confining walls with various anchoring conditions. We confirm the existence of a transition between a passive phase and an active phase, in which there is spontaneous flow in the steady state. This transition is attained for sufficiently ``extensile'' rods, in the case of flow-aligning liquid crystals, and for sufficiently ``contractile'' ones for flow-tumbling materials. In a quasi-1D geometry, deep in the active phase of flow-aligning materials, our simulations give evidence of hysteresis and history-dependent steady states, as well as of spontaneous banded flow. Flow-tumbling materials, in contrast, re-arrange themselves so that only the two boundary layers flow in steady state. Two-dimensional simulations, with periodic boundary conditions, show additional instabilities, with the spontaneous flow appearing as patterns made up of ``convection rolls''. These results demonstrate a remarkable richness (including dependence on anchoring conditions) in the steady-state phase behaviour of active materials, even in the absence of external forcing; they have no counterpart for passive nematics. Our HLB methodology, which combines lattice Boltzmann for momentum transport with a finite difference scheme for the order parameter dynamics, offers a robust and efficient method for probing the complex hydrodynamic behaviour of active nematics.Comment: 18 eps figures, accepted for publication in Phys. Rev.

Quantum ESPRESSO: One Further Step toward the Exascale

We review the status of the Quantum ESPRESSO software suite for electronic-structure calculations based on plane waves, pseudopotentials, and density-functional theory. We highlight the recent developments in the porting to GPUs of the main codes, using an approach based on OpenACC and CUDA Fortran offloading. We describe, in particular, the results achieved on linear-response codes, which are one of the distinctive features of the Quantum ESPRESSO suite. We also present extensive performance benchmarks on different GPU-accelerated architectures for the main codes of the suite

Structure and dynamics of ring polymers: entanglement effects because of solution density and ring topology

The effects of entanglement in solutions and melts of unknotted ring polymers have been addressed by several theoretical and numerical studies. The system properties have been typically profiled as a function of ring contour length at fixed solution density. Here, we use a different approach to investigate numerically the equilibrium and kinetic properties of solutions of model ring polymers. Specifically, the ring contour length is maintained fixed, while the interplay of inter- and intra-chain entanglement is modulated by varying both solution density (from infinite dilution up to \approx 40 % volume occupancy) and ring topology (by considering unknotted and trefoil-knotted chains). The equilibrium metric properties of rings with either topology are found to be only weakly affected by the increase of solution density. Even at the highest density, the average ring size, shape anisotropy and length of the knotted region differ at most by 40% from those of isolated rings. Conversely, kinetics are strongly affected by the degree of inter-chain entanglement: for both unknots and trefoils the characteristic times of ring size relaxation, reorientation and diffusion change by one order of magnitude across the considered range of concentrations. Yet, significant topology-dependent differences in kinetics are observed only for very dilute solutions (much below the ring overlap threshold). For knotted rings, the slowest kinetic process is found to correspond to the diffusion of the knotted region along the ring backbone.Comment: 17 pages, 11 figure

Lattice Boltzmann Simulations of Liquid Crystal Hydrodynamics

We describe a lattice Boltzmann algorithm to simulate liquid crystal hydrodynamics. The equations of motion are written in terms of a tensor order parameter. This allows both the isotropic and the nematic phases to be considered. Backflow effects and the hydrodynamics of topological defects are naturally included in the simulations, as are viscoelastic properties such as shear-thinning and shear-banding.Comment: 14 pages, 5 figures, Revte

The Lorentz Integral Transform (LIT) method and its applications to perturbation induced reactions

The LIT method has allowed ab initio calculations of electroweak cross sections in light nuclear systems. This review presents a description of the method from both a general and a more technical point of view, as well as a summary of the results obtained by its application. The remarkable features of the LIT approach, which make it particularly efficient in dealing with a general reaction involving continuum states, are underlined. Emphasis is given on the results obtained for electroweak cross sections of few--nucleon systems. Their implications for the present understanding of microscopic nuclear dynamics are discussed.Comment: 83 pages, 31 figures. Topical review. Corrected typo

Equilibrium shapes of flat knots

We study the equilibrium shapes of prime and composite knots confined to two dimensions. Using rigorous scaling arguments we show that, due to self-avoiding effects, the topological details of prime knots are localised on a small portion of the larger ring polymer. Within this region, the original knot configuration can assume a hierarchy of contracted shapes, the dominating one given by just one small loop. This hierarchy is investigated in detail for the flat trefoil knot, and corroborated by Monte Carlo simulations.Comment: 4 pages, 3 figure