Quantum Monte Carlo Study of High Pressure Solid Molecular Hydrogen

We use the diffusion quantum Monte Carlo (DMC) method to calculate the ground state phase diagram of solid molecular hydrogen and examine the stability of the most important insulating phases relative to metallic crystalline molecular hydrogen. We develop a new method to account for finite-size errors by combining the use of twist-averaged boundary conditions with corrections obtained using the Kwee-Zhang-Krakauer (KZK) functional in density functional theory. To study band-gap closure and find the metallization pressure, we perform accurate quasi-particle many-body calculations using the $GW$ method. In the static approximation, our DMC simulations indicate a transition from the insulating Cmca-12 structure to the metallic Cmca structure at around 375 GPa. The $GW$ band gap of Cmca-12 closes at roughly the same pressure. In the dynamic DMC phase diagram, which includes the effects of zero-point energy, the Cmca-12 structure remains stable up to 430 GPa, well above the pressure at which the $GW$ band gap closes. Our results predict that the semimetallic state observed experimentally at around 360 GPa [Phys. Rev. Lett. {\bf 108}, 146402 (2012)] may correspond to the Cmca-12 structure near the pressure at which the band gap closes. The dynamic DMC phase diagram indicates that the hexagonal close packed $P6_3/m$ structure, which has the largest band gap of the insulating structures considered, is stable up to 220 GPa. This is consistent with recent X-ray data taken at pressures up to 183 GPa [Phys. Rev. B {\bf 82}, 060101(R) (2010)], which also reported a hexagonal close packed arrangement of hydrogen molecules

Accurate exchange-correlation energies for the warm dense electron gas

Density matrix quantum Monte Carlo (DMQMC) is used to sample exact-on-average $N$-body density matrices for uniform electron gas systems of up to 10$^{124}$ matrix elements via a stochastic solution of the Bloch equation. The results of these calculations resolve a current debate over the accuracy of the data used to parametrize finite-temperature density functionals. Exchange-correlation energies calculated using the real-space restricted path-integral formalism and the $k$-space configuration path-integral formalism disagree by up to $\sim$$10$\% at certain reduced temperatures $T/T_F \le 0.5$ and densities $r_s \le 1$. Our calculations confirm the accuracy of the configuration path-integral Monte Carlo results available at high density and bridge the gap to lower densities, providing trustworthy data in the regime typical of planetary interiors and solids subject to laser irradiation. We demonstrate that DMQMC can calculate free energies directly and present exact free energies for $T/T_F \ge 1$ and $r_s \le 2$.Comment: Accepted version: added free energy data and restructured text. Now includes supplementary materia

Open-source development experiences in scientific software: the HANDE quantum Monte Carlo project

The HANDE quantum Monte Carlo project offers accessible stochastic algorithms for general use for scientists in the field of quantum chemistry. HANDE is an ambitious and general high-performance code developed by a geographically-dispersed team with a variety of backgrounds in computational science. In the course of preparing a public, open-source release, we have taken this opportunity to step back and look at what we have done and what we hope to do in the future. We pay particular attention to development processes, the approach taken to train students joining the project, and how a flat hierarchical structure aids communicationComment: 6 pages. Submission to WSSSPE

Developmental stage-specific regulation of the circadian Clock by Temperature in Zebrafish

The circadian clock enables animals to adapt their physiology and behaviour in anticipation of the day-night cycle. Light and temperature represent two key environmental timing cues (zeitgebers) able to reset this mechanism and so maintain its synchronization with the environmental cycle. One key challenge is to unravel how the regulation of the clock by zeitgebers matures during early development. The zebrafish is an ideal model for studying circadian clock ontogeny since the process of development occurs ex utero in an optically transparent chorion and many tools are available for genetic analysis. However, the role played by temperature in regulating the clock during zebrafish development is poorly understood. Here, we have established a clock-regulated luciferase reporter transgenic zebrafish line (Tg (−3.1) per1b::luc) to study the effects of temperature on clock entrainment. We reveal that under complete darkness, from an early developmental stage onwards (48 to 72 hpf), exposure to temperature cycles is a prerequisite for the establishment of self-sustaining rhythms of zfper1b, zfaanat2, and zfirbp expression and also for circadian cell cycle rhythms. Furthermore, we show that following the 5–9 somite stage, the expression of zfper1b is regulated by acute temperature shifts

Tolerance of septoria leaf blotch in winter wheat

For individual varieties, tolerance of septoria leaf blotch was quantified by the slope of the relationship between disease and yield. Variation in disease severity and the associated yield responses were provided across two sites and three seasons of field experiments. Slopes were fitted by residual maximum likelihood for two contrasting models: (i) a fixed-effects model, where no prior assumptions were made about the form of the variety slopes; and (ii) a random-effects model, where deviations in individual variety slopes away from the mean variety slope formed a normal random population with unknown variance. The analyses gave broadly similar results, but with some significant differences. The random model was considered more reliable for predicting variety performance. The effects of disease were quantified as symptom area and green canopy duration. Models of the relationship between symptom area and yield were site-specific. When site effects were not taken into account, these models had poor predictive precision. Models based on the canopy green area gave robust predictions of yield and were not site-specific. Differences in disease tolerance were detected in a comparison of 25 commercial winter wheat varieties. Tolerance was not detected directly through symptom measurements, but instead through measurements of canopy green area, which provides a measurement of the effects of disease that accounts for differences in canopy size across sites and seasons. The varieties showing greatest tolerance tended to have lower attainable yield than the intolerant varieties. Presence of the 1BL/1RS chromosome translocation, which has been reported to increase radiation use efficiency, appeared to be associated with intolerance

Riding a Spiral Wave: Numerical Simulation of Spiral Waves in a Co-Moving Frame of Reference

We describe an approach to numerical simulation of spiral waves dynamics of large spatial extent, using small computational grids.Comment: 15 pages, 14 figures, as accepted by Phys Rev E 2010/03/2

Discovering quantum phase transitions with fermionic neural networks

Deep neural networks have been extremely successful as highly accurate wave function ans\"atze for variational Monte Carlo calculations of molecular ground states. We present an extension of one such ansatz, FermiNet, to calculations of the ground states of periodic Hamiltonians, and study the homogeneous electron gas. FermiNet calculations of the ground-state energies of small electron gas systems are in excellent agreement with previous initiator full configuration interaction quantum Monte Carlo and diffusion Monte Carlo calculations. We investigate the spin-polarized homogeneous electron gas and demonstrate that the same neural network architecture is capable of accurately representing both the delocalized Fermi liquid state and the localized Wigner crystal state. The network is given no \emph{a priori} knowledge that a phase transition exists, but converges on the translationally invariant ground state at high density and spontaneously breaks the symmetry to produce the crystalline ground state at low density