Dynamic roughening of the magnetic flux landscape in YBa2_2Cu3_3O7−x_{7-x}

We study the magnetic flux landscape in YBa$_2$Cu$_3$O$_{7-x}$ thin films as a two dimensional rough surface. The vortex density in the superconductor forms a self-affine structure in both space and time. This is characterized by a roughness exponent $\alpha = 0.76(3)$ and a growth exponent $\beta = 0.57(6)$. This is due to the structure and distribution of flux avalanches in the self-organized critical state, which is formed in the superconductor. We also discuss our results in the context of other roughening systems in the presence of quenched disorder.Comment: 13 pages, 7 figures, accepted for publication in Physica

Significance of solutions of the inverse Biot-Savart problem in thick superconductors

The evaluation of current distributions in thick superconductors from field profiles near the sample surface is investigated theoretically. A simple model of a cylindrical sample, in which only circular currents are flowing, reduces the inversion to a linear least squares problem, which is analyzed by singular value decomposition. Without additional assumptions about the current distribution (e.g. constant current over the sample thickness), the condition of the problem is very bad, leading to unrealistic results. However, any additional assumption strongly influences the solution and thus renders the solutions again questionable. These difficulties are unfortunately inherent to the inverse Biot-Savart problem in thick superconductors and cannot be avoided by any models or algorithms

Evolving solitons in bubbly flows

At the end of the sixties, it was shown that pressure waves in a bubbly liquid obey the KdV equation, the nonlinear term coming from convective acceleration and the dispersive term from volume oscillations of the bubbles.\ud For a variableu, proportional to –p, wherep denotes pressure, the appropriate KdV equation can be casted in the formu t –6uu x +u xxx =0. The theory of this equation predicts that, under certain conditions, solitons evolve from an initial profileu(x,0). In particular, it can be shown that the numberN of those solitons can be found from solving the eigenvalue problem xx–u(x,0)=0, with(0)=1 and(0)=0.N is found from counting the zeros of the solution of this equation betweenx=0 andx=Q, say,Q being determined by the shape ofu(x,0). We took as an initial pressure profile a Shockwave, followed by an expansion wave. This can be realised in the laboratory and the problem, formulated above, can be solved exactly.\ud In this contribution the solution is outlined and it is shown from the experimental results that from the said initial disturbance, indeed solitons evolve in the predicated quantity.\u

Avalanches and Self-Organized Criticality in Superconductors

We review the use of superconductors as a playground for the experimental study of front roughening and avalanches. Using the magneto-optical technique, the spatial distribution of the vortex density in the sample is monitored as a function of time. The roughness and growth exponents corresponding to the vortex landscape are determined and compared to the exponents that characterize the avalanches in the framework of Self-Organized Criticality. For those situations where a thermo-magnetic instability arises, an analytical non-linear and non-local model is discussed, which is found to be consistent to great detail with the experimental results. On anisotropic substrates, the anisotropy regularizes the avalanches

A window into the neutron star: Modelling the cooling of accretion heated neutron star crusts

In accreting neutron star X-ray transients, the neutron star crust can be substantially heated out of thermal equilibrium with the core during an accretion outburst. The observed subsequent cooling in quiescence (when accretion has halted) offers a unique opportunity to study the structure and thermal properties of the crust. Initially crust cooling modelling studies focussed on transient X-ray binaries with prolonged accretion outbursts (> 1 year) such that the crust would be significantly heated for the cooling to be detectable. Here we present the results of applying a theoretical model to the observed cooling curve after a short accretion outburst of only ~10 weeks. In our study we use the 2010 outburst of the transiently accreting 11 Hz X-ray pulsar in the globular cluster Terzan 5. Observationally it was found that the crust in this source was still hot more than 4 years after the end of its short accretion outburst. From our modelling we found that such a long-lived hot crust implies some unusual crustal properties such as a very low thermal conductivity (> 10 times lower than determined for the other crust cooling sources). In addition, we present our preliminary results of the modelling of the ongoing cooling of the neutron star in MXB 1659-298. This transient X-ray source went back into quiescence in March 2017 after an accretion phase of ~1.8 years. We compare our predictions for the cooling curve after this outburst with the cooling curve of the same source obtained after its previous outburst which ended in 2001.Comment: 4 pages, 1 figure, to appear in the proceedings of "IAUS 337: Pulsar Astrophysics - The Next 50 Years" eds: P. Weltevrede, B.B.P. Perera, L. Levin Preston & S. Sanida

Oscillations of a gas pocket on a liquid-covered solid surface

The dynamic response of a gas bubble entrapped in a cavity on the surface of a submerged solid subject to an acoustic field is investigated in the linear approximation. We derive semi-analytical expressions for the resonance frequency, damping and interface shape of the bubble. For the liquid phase, we consider two limit cases: potential flow and unsteady Stokes flow. The oscillation frequency and interface shape are found to depend on two dimensionless parameters: the ratio of the gas stiffness to the surface tension stiffness, and the Ohnesorge number, representing the relative importance of viscous forces. We perform a parametric study and show, among others, that an increase in the gas pressure or a decrease in the surface tension leads to an increase in the resonance frequency until an asymptotic value is reached

Bubble size prediction in co-flowing streams

In this paper, the size of bubbles formed through the breakup of a gaseous jet in a co-axial microfluidic device is derived. The gaseous jet surrounded by a co-flowing liquid stream breaks up into monodisperse microbubbles and the size of the bubbles is determined by the radius of the inner gas jet and the bubble formation frequency. We obtain the radius of the gas jet by solving the Navier-Stokes equations for low Reynolds number flows and by minimization of the dissipation energy. The prediction of the bubble size is based on the system's control parameters only, i.e. the inner gas flow rate $Q_i$, the outer liquid flow rate $Q_o$, and the tube radius $R$. For a very low gas-to-liquid flow rate ratio ($Q_i / Q_o \rightarrow 0$) the bubble radius scales as $r_b / R \propto \sqrt{Q_i / Q_o}$, independently of the inner to outer viscosity ratio $\eta_i/\eta_o$ and of the type of the velocity profile in the gas, which can be either flat or parabolic, depending on whether high-molecular-weight surfactants cover the gas-liquid interface or not. However, in the case in which the gas velocity profiles are parabolic and the viscosity ratio is sufficiently low, i.e. $\eta_i/\eta_o \ll 1$, the bubble diameter scales as $r_b \propto (Q_i/Q_o)^\beta$, with $\beta$ smaller than 1/2

Dynamics of stripe patterns in type-I superconductors subject to a rotating field

The evolution of stripe patterns in type-I superconductors subject to a rotating in-plane magnetic field is investigated magneto-optically. The experimental results reveal a very rich and interesting behavior of the patterns. For small rotation angles, a small parallel displacement of the main part of the stripes and a co-rotation of their very ends is observed. For larger angles, small sideward protrusions develop, which then generate a zigzag instability, ultimately leading to a breaking of stripes into smaller segments. The short segments then start to co-rotate with the applied field although they lag behind by approximately $10^\circ$. Very interestingly, if the rotation is continued, also reconnection of segments into longer stripes takes place. These observations demonstrate the importance of pinning in type-I superconductors.Comment: To appear in Phys. Rev.