Free energy surface of ST2 water near the liquid-liquid phase transition

We carry out umbrella sampling Monte Carlo simulations to evaluate the free energy surface of the ST2 model of water as a function two order parameters, the density and a bond-orientational order parameter. We approximate the long-range electrostatic interactions of the ST2 model using the reaction-field method. We focus on state points in the vicinity of the liquid-liquid critical point proposed for this model in earlier work. At temperatures below the predicted critical temperature we find two basins in the free energy surface, both of which have liquid-like bond orientational order, but differing in density. The pressure and temperature dependence of the shape of the free energy surface is consistent with the assignment of these two basins to the distinct low density and high density liquid phases previously predicted to occur in ST2 water.Comment: 8 pages, 9 figure

Crystal Nucleation in a Supercooled Liquid with Glassy Dynamics

In simulations of supercooled, high-density liquid silica we study a range of temperature T in which we find both crystal nucleation, as well as the characteristic dynamics of a glass forming liquid, including a breakdown of the Stokes-Einstein relation. We find that the liquid cannot be observed below a homogeneous nucleation limit (HNL) at which the liquid crystallizes faster than it can equilibrate. We show that the HNL would occur at lower T, and perhaps not at all, if the Stokes-Einstein relation were obeyed, and hence that glassy dynamics plays a central role in setting a crystallization limit on the liquid state in this case. We also explore the relation of the HNL to the Kauzmann temperature, and test for spinodal-like effects near the HNL.Comment: 4 pages, 4 figure

"Swarm relaxation": Equilibrating a large ensemble of computer simulations

It is common practice in molecular dynamics and Monte Carlo computer simulations to run multiple, separately-initialized simulations in order to improve the sampling of independent microstates. Here we examine the utility of an extreme case of this strategy, in which we run a large ensemble of $M$ independent simulations (a "swarm"), each of which is relaxed to equilibrium. We show that if $M$ is of order $10^3$, we can monitor the swarm's relaxation to equilibrium, and confirm its attainment, within $\sim 10\bar\tau$, where $\bar\tau$ is the equilibrium relaxation time. As soon as a swarm of this size attains equilibrium, the ensemble of $M$ final microstates from each run is sufficient for the evaluation of most equilibrium properties without further sampling. This approach dramatically reduces the wall-clock time required, compared to a single long simulation, by a factor of several hundred, at the cost of an increase in the total computational effort by a small factor. It is also well-suited to modern computing systems having thousands of processors, and is a viable strategy for simulation studies that need to produce high-precision results in a minimum of wall-clock time. We present results obtained by applying this approach to several test cases.Comment: 12 pages. To appear in Eur. Phy. J. E, 201

Matrix bandwidth and profile reduction

This program, REDUCE, reduces the bandwidth and profile of sparse symmetric matrices, using row and corresponding column permutations. It is a realization of the algorithm described by the authors elsewhere. It was extensively tested and compared with several other programs and was found to be considerably faster than the others, superior for bandwidth reduction and as satisfactory as any other for profile reduction

Weak inter-band coupling in Mg10^{10}B2_{2}: a specific heat analysis

The superconducting state of Mg$^{10}$B$_{2}$ is investigated by specific heat measurements in detail. The specific heat in the normal state is analyzed using a recently developed computer code. This allows for an extraction of the electronic specific heat in the superconducting state with high accuracy and a fair determination of the main lattice features. One of the two investigated samples shows a hump in the specific heat at low temperatures within the superconducting state, accompanied by an unusual low value of the small gap, $\Delta_{\pi}(0)=1.32 meV$, pointing to a very weak inter-band coupling. This sample allows for a detailed analysis of the contribution from the $\pi$-band to the electronic specific heat in the superconducting state. Therefore the usual analysis method is modified, to include the individual conservation of entropy of both bands. From analyzing the deviation function $D(t)$ of MgB$_{2}$, the theoretically predicted weak inter-band coupling scenario is confirmed.Comment: major revision

Coplanar stripline antenna design for optically detected magnetic resonance on semiconductor quantum dots

We report on the development and testing of a coplanar stripline antenna that is designed for integration in a magneto-photoluminescence experiment to allow coherent control of individual electron spins confined in single self-assembled semiconductor quantum dots. We discuss the design criteria for such a structure which is multi-functional in the sense that it serves not only as microwave delivery but also as electrical top gate and shadow mask for the single quantum dot spectroscopy. We present test measurements on hydrogenated amorphous silicon, demonstrating electrically detected magnetic resonance using the in-plane component of the oscillating magnetic field created by the coplanar stripline antenna necessary due to the particular geometry of the quantum dot spectroscopy. From reference measurements using a commercial electron spin resonance setup in combination with finite element calculations simulating the field distribution in the structure, we obtain an average magnetic field of ~0.2mT at the position where the quantum dots would be integrated into the device. The corresponding pi-pulse time of ~0.3us fully meets the requirements set by the high sensitivity optical spin read-out scheme developed for the quantum dot

Detection of single electron spin resonance in a double quantum dot

Spin-dependent transport measurements through a double quantum dot are a valuable tool for detecting both the coherent evolution of the spin state of a single electron as well as the hybridization of two-electron spin states. In this paper, we discuss a model that describes the transport cycle in this regime, including the effects of an oscillating magnetic field (causing electron spin resonance) and the effective nuclear fields on the spin states in the two dots. We numerically calculate the current flow due to the induced spin flips via electron spin resonance and we study the detector efficiency for a range of parameters. The experimental data are compared with the model and we find a reasonable agreement.Comment: 7 pages, 5 figures. To be published in Journal of Applied Physics, proceedings ICPS 200

The Influence of Game Demand on Distraction from Experimental Pain: A fNIRS Study

Video games are the most effective form of distraction from procedural pain compared to other distraction techniques, such as watching television or reading a book (Hussein, 2015). The degree of cognitive engagement with the game is a strong influence on the capacity of game-playing to distract from pain. By increasing game demand to a level that demands maximum levels of attention, it is possible to optimise distraction from pain; however, if the game becomes too difficult, it will fail to act as a distraction

Test of classical nucleation theory on deeply supercooled high-pressure simulated silica

We test classical nucleation theory (CNT) in the case of simulations of deeply supercooled, high density liquid silica, as modelled by the BKS potential. We find that at density $\rho=4.38$~g/cm$^3$, spontaneous nucleation of crystalline stishovite occurs in conventional molecular dynamics simulations at temperature T=3000 K, and we evaluate the nucleation rate J directly at this T via "brute force" sampling of nucleation events. We then use parallel, constrained Monte Carlo simulations to evaluate $\Delta G(n)$, the free energy to form a crystalline embryo containing n silicon atoms, at T=3000, 3100, 3200 and 3300 K. We find that the prediction of CNT for the n-dependence of $\Delta G(n)$ fits reasonably well to the data at all T studied, and at 3300 K yields a chemical potential difference between liquid and stishovite that matches independent calculation. We find that $n^*$, the size of the critical nucleus, is approximately 10 silicon atoms at T=3300 K. At 3000 K, $n^*$ decreases to approximately 3, and at such small sizes methodological challenges arise in the evaluation of $\Delta G(n)$ when using standard techniques; indeed even the thermodynamic stability of the supercooled liquid comes into question under these conditions. We therefore present a modified approach that permits an estimation of $\Delta G(n)$ at 3000 K. Finally, we directly evaluate at T=3000 K the kinetic prefactors in the CNT expression for J, and find physically reasonable values; e.g. the diffusion length that Si atoms must travel in order to move from the liquid to the crystal embryo is approximately 0.2 nm. We are thereby able to compare the results for J at 3000 K obtained both directly and based on CNT, and find that they agree within an order of magnitude.Comment: corrected calculation, new figure, accepted in JC

Magnetic levitation on a type-I superconductor as a practical demonstration experiment for students

We describe and discuss an experimental set-up which allows undergraduate and graduate students to view and study magnetic levitation on a type-I superconductor. The demonstration can be repeated many times using one readily available 25 liter liquid helium dewar. We study the equilibrium position of a magnet that levitates over a lead bowl immersed in a liquid hand-held helium cryostat. We combine the measurement of the position of the magnet with simple analytical calculations. This provides a vivid visualization of magnetic levitation from the balance between pure flux expulsion and gravitation. The experiment contrasts and illustrates the case of magnetic levitation with high temperature type-II superconductors using liquid nitrogen, where levitation results from partial flux expulsion and vortex physics