Anomalous scaling dimensions and critical points in type-II superconductors

The existence of a {\it stable critical point}, separate from the Gaussian and XY critical points, of the Ginzburg-Landau theory for superconductors, is demonstrated by direct extraction via Monte-Carlo simulations, of a negative anomalous dimension $\eta_{\phi}$ of a complex scalar field $\phi$ forming a dual description of a neutral superfluid. The dual of the neutral superfluid is isomorphic to a charged superfluid coupled to a massless gauge-field. The anomalous scaling dimension of the superfluid order-field is positive, while we find that the anomalous dimension of the dual field is negative. The dual gauge-field does not decouple from the dual complex matter-field at the critical point. {\it These two critical theories represent separate fixed points.} The physical meaning of a negative $\eta_{\phi}$ is that the vortex-loop tangle of the superfluid at the critical point fills space {\it more} efficiently than random walkers, {\it without collapsing}. This is due to the presence of the massless dual gauge-field, and the resulting long-ranged {\it vectorial} Biot-Savart interaction between vortex-loop segments, which is a relevant perturbation to the steric $|\psi|^4$ repulsion term. Hence, the critical dual theory is not in the universality class of the $|\psi|^4$-theory.Comment: 2 pages, 1 figur

The Open Porous Media Flow Reservoir Simulator

The Open Porous Media (OPM) initiative is a community effort that encourages open innovation and reproducible research for simulation of porous media processes. OPM coordinates collaborative software development, maintains and distributes open-source software and open data sets, and seeks to ensure that these are available under a free license in a long-term perspective. In this paper, we present OPM Flow, which is a reservoir simulator developed for industrial use, as well as some of the individual components used to make OPM Flow. The descriptions apply to the 2019.10 release of OPM.Comment: 43 pages, 22 figure

The number of link and cluster states: the core of the 2D q state Potts model

Due to Fortuin and Kastelyin the q state Potts model has a representation as a sum over random graphs, generalizing the Potts model to arbitrary q is based on this representation. A key element of the random cluster representation is the combinatorial factor ΓG(C, E), which is the number of ways to form C distinct clusters, consisting of totally E edges. We have devised a method to calculate ΓG(C, E) from Monte Carlo simulations

Dynamics of a CO2-seawater interface in the deep ocean

A trough filled with liquid CO2 located at 3940 m depth has been used as a model system for CO2 deposition on the seafloor. To study the intrinsic properties of the interface between CO2 and seawater a wave maker was used to excite regular plane waves. The frequency (≤2.5 rad/s) and wavelength (20 cm-40 cm) of the waves have been measured, and compare reasonably well with the dispersion relation for deep fluid gravity waves. The shear stability of the interface was investigated by setting the water above the CO2 in motion with a thruster. For shear velocities exceeding νc ≈ 17.6 cm/s the interface became unstable, with breaking waves and CO2 droplets torn from the wave crests. For the sheared system we find that the energy spectrum of the interface variations has a peak for wavelength ≈0.8 cm, meaning that energy absorption is greatest for this wavelength. For the most unstable wavelength of the Kelvin-Helmholtz instability to match this wavelength, an effective interfacial tension of the hydrate covered interface of γ ≈ 0.075 N/m must be assumed

Critical Properties of the Abelian Higgs Model. : A Monte Carlo Study

We have studied various aspects of the critical properties of the Abelian Higgs model. The initial motivation to study this model is its relation to superconductivity, but the results extend beyond the realms of superconductivity. This thesis contains an introductory part and three research papers, all related to different aspects of the Abelian Higgs model. Paper 1: We have investigated the properties of the model using a dual vortex representation. By focusing on the propagators of the gauge field <b>A</b> and the dual gauge field <b>h</b> we find a nice demonstration of the fact that the dual of a neutral condensate is isomorphic to a charged condensate. Finally this also provides firm support for the existence of a stable charged fixed point in the theory, distinct from the 3DXY fixed point. Paper 2: The critical fluctuations in the Abelian Higgs model are vortex loops. We have studied the geometrical properties of these loops, and by using duality we have obtained scaling relations between the fractal dimension DH of the loops and the anomalous dimension ηφ of the dual field theory. Paper 3: We have calculated the GL parameter κtri separating a first order metal to superconductor transition from a second order one, κtri =(0.76±0.04))/√2. We also argue qualitatively that this κtri is the value separating type-I and type-II behavior, in contrast to the conventional value 1=√2. The calculations have been done including fluctuations in the amplitude and the phase of the matter-field, as well as fluctuations in the gauge field. Paper 4: We have determined the effective interaction between vortices in the Ginzburg-Landau model from large-scale Monte-Carlo simulations. We find a change, in the form of a crossover, from attractive to repulsive effective vortex interactions in an intermediate range of Ginzburg-Landau parameters κε[0.76; 1]=√2, depending on temperature. We present a simple physical picture of the crossover, and relate it to observations in Ta and Nb elemental superconductors which have low-temperature values of κ in the relevant range.Papers I - 4 reprinted with kind permission of the American Physical Society. Copyright the American Physical Society

Scheduling ships with uncertain arrival times through the Kiel Canal

The Kiel Canal is a two-way waterway that connects the Baltic Sea and the North Sea. The canal consists of an alternating sequence of narrow transit segments and wider siding segments. This calls for solving a ship scheduling problem to decide which ships have to wait in sidings to let opposing traffic pass through such that the total traversing time of all ships is minimized. This paper extends previous studies on scheduling ships through the Kiel Canal by considering that the arrival times of the ships at the entrance to the canal are subject to uncertainty. This is a major challenge in the planning as it gives frequent need of replanning to make the schedules feasible. We propose a mathematical formulation for the problem to mitigate the negative effects of the uncertainty. This formulation incorporates time-corridors, so that the schedule will still be valid as long as the ships arrive within their given time-corridors. To solve real-sized instances of the problem, we adapt a matheuristic that adds violated constraints iteratively to the problem. The matheuristic was tested within a rolling horizon simulation framework to study the effect of arrival time uncertainty. We show by experiment that solutions of the matheuristic for different time-corridor widths can be used to identify a suitable corridor width that trades off the average traversing time of ships and the number of reschedules required in the planning. A simple myopic heuristic, reflecting the current scheduling practice, was used to generate benchmark results, and tests on real data showed that the matheuristic provides solutions with significantly less need of replanning, while at the same time keeping the total traversing times for the ships short. We also provide simulations to gain insight about the effect on the ships’ average traversing time from upgrading the narrow transit segments

The phase-field theory applied to CO2 and CH4 hydrate

A phase-field theory is applied to model the growth of carbon dioxide hydrate and methane hydrate from a supersaturated solution in water. Temperature- and pressure-dependent thermodynamics for the two systems are accounted for. Simulations of the growth of a planar hydrate film and a circular hydrate nucleus are presented and the interface velocity has been extrapolated from the results to experimental time scales. We discuss how pressure and temperature affects the growth rate and argue that the governing process for the dynamics is the chemical diffusion of the guest molecule in the aqueous solution. We also present results from anisotropic simulations and outline how this will affect the growth

Ocean abyssal carbon experiments at 0.7 and 4 km depth

Observations from small-scale (20 to 90 litres) CO2 experiments conducted off the coast of California at 684 m depth and at 3942 m depth are discussed. In both experiments, when the seawater velocity was sufficiently strong, parcels of liquid CO2 were torn off and transported away as discrete units by the turbulent water current. In the deep experiment, newly formed frazil hydrate was observed at the interface, occasionally including sediment particles. Hydrate furthermore collected and created a floating consolidated solid ("ice") in the downstream end of the trough, dissolving slowly from one day to the next. These observations have important implications for understanding and modelling of larger scale disposal at the seafloor. In particular, when CO2 is released by the interfacial instability mechanism driven by strong currents, the seawater density increase due to dissolution of CO2 may not have time to act and stabilize the water column before the discrete parcels of liquid phase CO2 are advected away from the disposal site. The floating solid that formed at the interface is hypothesized to consist of hydrate and additional trapped seawater. Its appearance was not expected in advance and its role in delaying dissolution can not be determined from the present experimental set-up. A capability for long-term seafloor perturbation experiments is deemed to be crucial both for direct ocean-storage research and for studying effects of invasion of anthropogenic CO2 from the atmosphere