Triadic resonances in non-linear simulations of a fluid flow in a precessing cylinder

We present results from three-dimensional non-linear hydrodynamic simulations of a precession driven flow in cylindrical geometry. The simulations are motivated by a dynamo experiment currently under development at Helmholtz-Zentrum Dresden-Rossendorf (HZDR) in which the possibility of generating a magnetohydrodynamic dynamo will be investigated in a cylinder filled with liquid sodium and simultaneously rotating around two axes. In this study, we focus on the emergence of non-axisymmetric time-dependent flow structures in terms of inertial waves which - in cylindrical geometry - form so-called Kelvin modes. For a precession ratio ${\rm{Po}}=\Omega_p/\Omega_c=0.014$ the amplitude of the forced Kelvin mode reaches up to one fourth of the rotation velocity of the cylindrical container confirming that precession provides a rather efficient flow driving mechanism even at moderate values of ${\rm{Po}}$. More relevant for dynamo action might be free Kelvin modes with higher azimuthal wave number. These free Kelvin modes are triggered by non-linear interactions and may constitute a triadic resonance with the fundamental forced mode when the height of the container matches their axial wave lengths. Our simulations reveal triadic resonances at aspect ratios close to those predicted by the linear theory except around the primary resonance of the forced mode. In that regime we still identify various free Kelvin modes, however, all of them exhibit a retrograde drift around the symmetry axis of the cylinder and none of them can be assigned to a triadic resonance. The amplitudes of the free Kelvin modes always remain below the forced mode but may reach up to 6% of the of the container's angular velocity. The properties of the free Kelvin modes will be used in future simulations of the magnetic induction equation to investigate their ability to provide for dynamo action.Comment: 26 pages, 14 figures, submitted to New J. Phy

Efficient local strategies for vaccination and network attack

We study how a fraction of a population should be vaccinated to most efficiently top epidemics. We argue that only local information (about the neighborhood of specific vertices) is usable in practice, and hence we consider only local vaccination strategies. The efficiency of the vaccination strategies is investigated with both static and dynamical measures. Among other things we find that the most efficient strategy for many real-world situations is to iteratively vaccinate the neighbor of the previous vaccinee that has most links out of the neighborhood

Electromagnetic induction in non-uniform domains

Kinematic simulations of the induction equation are carried out for different setups suitable for the von-K\'arm\'an-Sodium (VKS) dynamo experiment. Material properties of the flow driving impellers are considered by means of high conducting and high permeability disks that are present in a cylindrical volume filled with a conducting fluid. Two entirely different numerical codes are mutually validated by showing quantitative agreement on Ohmic decay and kinematic dynamo problems using various configurations and physical parameters. Field geometry and growth rates are strongly modified by the material properties of the disks even if the high permeability/high conductivity material is localized within a quite thin region. In contrast the influence of external boundary conditions remains small. Utilizing a VKS like mean fluid flow and high permeability disks yields a reduction of the critical magnetic Reynolds number for the onset of dynamo action of the simplest non-axisymmetric field mode. However this decrease is not sufficient to become relevant in the VKS experiment. Furthermore, the reduction of Rm_c is essentially influenced by tiny changes in the flow configuration so that the result is not very robust against small modifications of setup and properties of turbulence

Towards a precession driven dynamo experiment

The most ambitious project within the DREsden Sodium facility for DYNamo and thermohydraulic studies (DRESDYN) at Helmholtz-Zentrum Dresden-Rossendorf (HZDR) is the set-up of a precession-driven dynamo experiment. After discussing the scientific background and some results of water pre-experiments and numerical predictions, we focus on the numerous structural and design problems of the machine. We also outline the progress of the building's construction, and the status of some other experiments that are planned in the framework of DRESDYN.Comment: 9 pages, 6 figures, submitted to Magnetohydrodynamic

The microgravity environment of the Space Shuttle Columbia payload bay during STS-32

Over 11 hours of three-axis microgravity accelerometer data were successfully measured in the payload bay of Space Shuttle Columbia as part of the Microgravity Disturbances Experiment on STS-32. These data were measured using the High Resolution Accelerometer Package and the Aerodynamic Coefficient Identification Package which were mounted on the Orbiter keel in the aft payload bay. Data were recorded during specific mission events such as Orbiter quiescent periods, crew exercise on the treadmill, and numerous Orbiter engine burns. Orbiter background levels were measured in the 10(exp -5) G range, treadmill operations in the 10(exp -3) G range, and the Orbiter engine burns in the 10(exp -2) G range. Induced acceleration levels resulting from the SYNCOM satellite deploy were in the 10 (exp -2) G range, and operations during the pre-entry Flight Control System checkout were in the 10(exp -2) to 10(exp -1) G range

Systemic Risk and Default Clustering for Large Financial Systems

As it is known in the finance risk and macroeconomics literature, risk-sharing in large portfolios may increase the probability of creation of default clusters and of systemic risk. We review recent developments on mathematical and computational tools for the quantification of such phenomena. Limiting analysis such as law of large numbers and central limit theorems allow to approximate the distribution in large systems and study quantities such as the loss distribution in large portfolios. Large deviations analysis allow us to study the tail of the loss distribution and to identify pathways to default clustering. Sensitivity analysis allows to understand the most likely ways in which different effects, such as contagion and systematic risks, combine to lead to large default rates. Such results could give useful insights into how to optimally safeguard against such events.Comment: in Large Deviations and Asymptotic Methods in Finance, (Editors: P. Friz, J. Gatheral, A. Gulisashvili, A. Jacqier, J. Teichmann) , Springer Proceedings in Mathematics and Statistics, Vol. 110 2015

Synthetic protein–protein interaction domains created by shuffling Cys(2)His(2) zinc-fingers

Cys(2)His(2) zinc-fingers (C2H2 ZFs) mediate a wide variety of protein–DNA and protein–protein interactions. DNA-binding C2H2 ZFs can be shuffled to yield artificial proteins with different DNA-binding specificities. Here we demonstrate that shuffling of C2H2 ZFs from transcription factor dimerization zinc-finger (DZF) domains can also yield two-finger DZFs with novel protein–protein interaction specificities. We show that these synthetic protein–protein interaction domains can be used to mediate activation of a single-copy reporter gene in bacterial cells and of an endogenous gene in human cells. In addition, the synthetic two-finger domains we constructed can also be linked together to create more extended, four-finger interfaces. Our results demonstrate that shuffling of C2H2 ZFs can yield artificial protein-interaction components that should be useful for applications in synthetic biology

Influence of high permeability disks in an axisymmetric model of the Cadarache dynamo experiment

Numerical simulations of the kinematic induction equation are performed on a model configuration of the Cadarache von-K\'arm\'an-Sodium dynamo experiment. The effect of a localized axisymmetric distribution of relative permeability {\mu} that represents soft iron material within the conducting fluid flow is investigated. The critical magnetic Reynolds number Rm^c for dynamo action of the first non-axisymmetric mode roughly scales like Rm^c({\mu})-Rm^c({\mu}->infinity) ~ {\mu}^(-1/2) i.e. the threshold decreases as {\mu} increases. This scaling law suggests a skin effect mechanism in the soft iron disks. More important with regard to the Cadarache dynamo experiment, we observe a purely toroidal axisymmetric mode localized in the high permeability disks which becomes dominant for large {\mu}. In this limit, the toroidal mode is close to the onset of dynamo action with a (negative) growth-rate that is rather independent of the magnetic Reynolds number. We qualitatively explain this effect by paramagnetic pumping at the fluid/disk interface and propose a simplified model that quantitatively reproduces numerical results. The crucial role of the high permeability disks for the mode selection in the Cadarache dynamo experiment cannot be inferred from computations using idealized pseudo-vacuum boundary conditions (H x n = 0).Comment: 16 pages, 9 Figures, published in New Journal of Physics 14(2012), 05300

The influence of current collectors on Tayler instability and electro-vortex flows in liquid metal batteries

The Tayler instability is a kink-type flow instability which occurs when the electrical current through a conducting fluid exceeds a certain critical value. Originally studied in the astrophysical context, the instability was recently shown to be also a limiting factor for the upward scalability of liquid metal batteries. In this paper, we continue our efforts to simulate this instability for liquid metals within the framework of an integro-differential equation approach. The original solver is enhanced by multi-domain support with Dirichlet-Neumann partitioning for the static boundaries. Particular focus is laid on the detailed influence of the axial electrical boundary conditions on the characteristic features of the Tayler instability, and, secondly, on the occurrence of electro-vortex flows and their relevance for liquid metal batteries.Comment: 26 pages, 16 figure