Pressure-energy correlations in liquids. V. Isomorphs in generalized Lennard-Jones systems

This series of papers is devoted to identifying and explaining the properties of strongly correlating liquids, i.e., liquids with more than 90% correlation between their virial W and potential energy U fluctuations in the NVT ensemble. Paper IV [N. Gnan et al., J. Chem. Phys. v131, 234504 (2009)] showed that strongly correlating liquids have "isomorphs", which are curves in the phase diagram along which structure, dynamics, and some thermodynamic properties are invariant in reduced units. In the present paper, using the fact that reduced-unit radial distribution functions are isomorph invariant, we derive an expression for the shapes of isomorphs in the WU phase diagram of generalized Lennard-Jones systems of one or more types of particles. The isomorph shape depends only on the Lennard-Jones exponents; thus all isomorphs of standard Lennard-Jones systems (with exponents 12 and 6) can be scaled onto to a single curve. Two applications are given. One is testing the prediction that the solid-liquid coexistence curve follows an isomorph by comparing to recent simulations by Ahmed and Sadus [J. Chem. Phys. v131, 174504 (2009)]. Excellent agreement is found on the liquid side of the coexistence, whereas the agreement is worse on the solid side. A second application is the derivation of an approximate equation of state for generalized Lennard-Jones systems by combining the isomorph theory with the Rosenfeld-Tarazona expression for the temperature dependence of potential energy on isochores. It is shown that the new equation of state agrees well with simulations.Comment: 12 pages, 14 figures, Section on solid-liquid coexistence expande

A randomised feasibility trial of an intervention to support sharing of HIV status for 18-25-year olds living with perinatally acquired HIV compared with standard care: HIV Empowering Adults' Decisions to Share-UK/Uganda Project (HEADS-UP)

Abstract: Background: Young adults with perinatally acquired HIV (PAH) face several challenges, including adhering to antiretroviral therapy (ART), managing the risk of onward HIV transmission and maintaining positive well-being. Sharing one's HIV status with others (onward HIV disclosure) may assist with these challenges by facilitating emotional and practical support. Rates of HIV status sharing are, however, low in this population. There are no existing interventions focused on sharing one's HIV status for young adults living with PAH. The HEADS-UP study is designed to develop and test the feasibility of an intervention to help the sharing of HIV status for young adults with PAH. Methods: The study is a 30-month multi-site randomised feasibility study across both a high-income/low-HIV prevalence country (UK) and a low-income/high-HIV prevalence country (Uganda). Phase 1 (12 months) will involve developing the intervention using qualitative interviews with 20 young people living with PAH (ten in the UK-18 to 29 years; ten in Uganda-18 to 25 years), 20 of their social network (friends, family, sexual partners as defined by the young person; ten in the UK, ten in Uganda) and ten professionals with experience working with young adults with PAH (five in the UK, five in Uganda). Phase 2 (18 months) involves conducting a randomised feasibility parallel group trial of the intervention alongside current standard of care condition in each country (main study) with 18- to 25-year olds with PAH. A sample size of 94 participants per condition (intervention or standard of care; 188 participants in total: 47 in each condition in each country) with data at both the baseline and 6-month follow-up time points, across UK and Ugandan sites will be recruited. Participants in the intervention condition will also complete measures immediately post-intervention. Face-to-face interviews will be conducted with ten participants in both countries immediately post-intervention and at 6-month follow-up (sub-study). Discussion: This study will be the first trial that we are aware of to address important gaps in understanding acceptable and feasible ways of delivering HIV status sharing support for young people living with PAH. Trial registration: ISRCTN Registry, ISRCTN31852047, Registered on 21 January, 2019. Study sponsor: Royal Holloway University of London. Sponsor contact: [email protected]. Date and version: April 2020. Protocol version 3.5

The Genetic Basis of Natural Variation in Seed Size and Seed Number and Their Trade-Off Using Arabidopsis thaliana MAGIC Lines

Offspring number and size are key traits determining an individual’s fitness and a crop’s yield. Yet, extensive natural variation within species is observed for these traits. Such variation is typically explained by trade-offs between fecundity and quality, for which an optimal solution is environmentally dependent. Understanding the genetic basis of seed size and number, as well as any possible genetic constraints preventing the maximization of both, is crucial from both an evolutionary and applied perspective. We investigated the genetic basis of natural variation in seed size and number using a set of Arabidopsis thaliana multiparent advanced generation intercross (MAGIC) lines. We also tested whether life history affects seed size, number, and their trade-off. We found that both seed size and seed number are affected by a large number of mostly nonoverlapping QTL, suggesting that seed size and seed number can evolve independently. The allele that increases seed size at most identified QTL is from the same natural accession, indicating past occurrence of directional selection for seed size. Although a significant trade-off between seed size and number is observed, its expression depends on life-history characteristics, and generally explains little variance. We conclude that the trade-off between seed size and number might have a minor role in explaining the maintenance of variation in seed size and number, and that seed size could be a valid target for selection

Modelling of photonic wire Bragg Gratings

Some important properties of photonic wire Bragg grating structures have been investigate. The design, obtained as a generalisation of the full-width gap grating, has been modelled using 3D finite-difference time-domain simulations. Different types of stop-band have been observed. The impact of the grating geometry on the lowest order (longest wavelength) stop-band has been investigated - and has identified deeply indented configurations where reduction of the stop-bandwidth and of the reflectivity occurred. Our computational results have been substantially validated by an experimental demonstration of the fundamental stop-band of photonic wire Bragg gratings fabricated on silicon-on-insulator material. The accuracy of two distinct 2D computational models based on the effective index method has also been studied - because of their inherently much greater rapidity and consequent utility for approximate initial designs. A 2D plan-view model has been found to reproduce a large part of the essential features of the spectral response of full 3D models

Isomorphs in model molecular liquids

Isomorphs are curves in the phase diagram along which a number of static and dynamic quantities are invariant in reduced units. A liquid has good isomorphs if and only if it is strongly correlating, i.e., the equilibrium virial/potential energy fluctuations are more than 90% correlated in the NVT ensemble. This paper generalizes isomorphs to liquids composed of rigid molecules and study the isomorphs of two systems of small rigid molecules, the asymmetric dumbbell model and the Lewis-Wahnstrom OTP model. In particular, for both systems we find that the isochoric heat capacity, the excess entropy, the reduced molecular center-of-mass self part of the intermediate scattering function, the reduced molecular center-of-mass radial distribution function to a good approximation are invariant along an isomorph. In agreement with theory, we also find that an instantaneous change of temperature and density from an equilibrated state point to another isomorphic state point leads to no relaxation. The isomorphs of the Lewis-Wahnstrom OTP model were found to be more approximative than those of the asymmetric dumbbell model, which is consistent with the OTP model being less strongly correlating. For both models we find "master isomorphs", i.e., isomorphs have identical shape in the virial/potential energy phase diagram.Comment: 20 page

Relationship between Structure, Entropy and Diffusivity in Water and Water-like Liquids

Anomalous behaviour of the excess entropy ($S_e$) and the associated scaling relationship with diffusivity are compared in liquids with very different underlying interactions but similar water-like anomalies: water (SPC/E and TIP3P models), tetrahedral ionic melts (SiO$_2$ and BeF$_2$) and a fluid with core-softened, two-scale ramp (2SRP) interactions. We demonstrate the presence of an excess entropy anomaly in the two water models. Using length and energy scales appropriate for onset of anomalous behaviour, the density range of the excess entropy anomaly is shown to be much narrower in water than in ionic melts or the 2SRP fluid. While the reduced diffusivities ($D^*$) conform to the excess entropy scaling relation, $D^* =A\exp (\alpha S_e)$ for all the systems (Y. Rosenfeld, Phys. Rev. A {\bf 1977}, {\it 15}, 2545), the exponential scaling parameter, $\alpha$, shows a small isochore-dependence in the case of water. Replacing $S_e$ by pair correlation-based approximants accentuates the isochore-dependence of the diffusivity scaling. Isochores with similar diffusivity scaling parameters are shown to have the temperature dependence of the corresponding entropic contribution. The relationship between diffusivity, excess entropy and pair correlation approximants to the excess entropy are very similar in all the tetrahedral liquids.Comment: 24 pages, 4 figures, to be published in Journal of Physical Chemistry

Volume-energy correlations in the slow degrees of freedom of computer-simulated phospholipid membranes

Constant-pressure molecular-dynamics simulations of phospholipid membranes in the fluid phase reveal strong correlations between equilibrium fluctuations of volume and energy on the nanosecond time-scale. The existence of strong volume-energy correlations was previously deduced indirectly by Heimburg from experiments focusing on the phase transition between the fluid and the ordered gel phases. The correlations, which are reported here for three different membranes (DMPC, DMPS-Na, and DMPSH), have volume-energy correlation coefficients ranging from 0.81 to 0.89. The DMPC membrane was studied at two temperatures showing that the correlation coefficient increases as the phase transition is approached

Pressure-energy correlations in liquids. II. Analysis and consequences

We present an analysis and discuss consequences of the strong correlations of the configurational parts of pressure and energy in their equilibrium fluctuations at fixed volume reported for simulations of several liquids in the companion paper [arXiv:0807.0550]. The analysis concentrates specifically on the single-component Lennard-Jones system. We demonstrate that the potential may be replaced, at fixed volume, by an effective power-law, but not because only short distance encounters dominate the fluctuations. Indeed, contributions to the fluctuations are associated with the whole first peak of the RDF, as we demonstrate by an analysis of the spatially resolved covariance matrix. The reason the effective power-law works so well depends on going beyond single-pair effects and on the constraint of fixed volume. In particular, a better approximation to the potential includes a linear term, which contributes to the mean values of potential energy and virial, but not to their fluctuations. We also study the T=0 limit of the crystalline phase, where the correlation coefficient becomes very close, but not equal, to unity. We then consider four consequences of strong pressure-energy correlations: (1) analyzing experimental data for supercritical Ar we find 96% correlation; (2) we discuss the significance acquired by the correlations for viscous van der Waals liquids approaching the glass transition: For strongly correlating viscous liquids knowledge of just one of the eight frequency-dependent thermoviscoelastic response functions basically implies knowledge of them all; (3) we re-interpret aging simulations of ortho-terphenyl carried out by Mossa {\it et al.} in 2002, showing their conclusions follow from the strongly correlating property; and (4) we discuss correlations in model biomembranes.Comment: Some changes corresponding to those made in the proof of the accepted articl

On-chip quantum interference between silicon photon-pair sources

Large-scale integrated quantum photonic technologies will require the on-chip integration of identical photon sources with reconfigurable waveguide circuits. Relatively complex quantum circuits have already been demonstrated, but few studies acknowledge the pressing need to integrate photon sources and waveguide circuits together on-chip. A key step towards such large-scale quantum technologies is the integration of just two individual photon sources within a waveguide circuit, and the demonstration of high-visibility quantum interference between them. Here, we report a silicon-on-insulator device combining two four-wave mixing sources, in an interferometer with a reconfigurable phase shifter. We configure the device to create and manipulate two-colour (non-degenerate) or same-colour (degenerate), path-entangled or path-unentangled photon pairs. We observe up to 100.0+/-0.4% visibility quantum interference on-chip, and up to 95+/-4% off-chip. Our device removes the need for external photon sources, provides a path to increasing the complexity of quantum photonic circuits, and is a first step towards fully-integrated quantum technologies