Exploring helical dynamos with machine learning

We use ensemble machine learning algorithms to study the evolution of magnetic fields in magnetohydrodynamic (MHD) turbulence that is helically forced. We perform direct numerical simulations of helically forced turbulence using mean field formalism, with electromotive force (EMF) modeled both as a linear and non-linear function of the mean magnetic field and current density. The form of the EMF is determined using regularized linear regression and random forests. We also compare various analytical models to the data using Bayesian inference with Markov Chain Monte Carlo (MCMC) sampling. Our results demonstrate that linear regression is largely successful at predicting the EMF and the use of more sophisticated algorithms (random forests, MCMC) do not lead to significant improvement in the fits. We conclude that the data we are looking at is effectively low dimensional and essentially linear. Finally, to encourage further exploration by the community, we provide all of our simulation data and analysis scripts as open source IPython notebooks.Comment: accepted by A&A, 11 pages, 6 figures, 3 tables, data + IPython notebooks: https://github.com/fnauman/ML_alpha

Sustained Turbulence in Differentially Rotating Magnetized Fluids at Low Magnetic Prandtl Number

We show for the first time that sustained turbulence is possible at low magnetic Prandtl number for Keplerian flows with no mean magnetic flux. Our results indicate that increasing the vertical domain size is equivalent to increasing the dynamical range between the energy injection scale and the dissipative scale. This has important implications for a large variety of differentially rotating systems with low magnetic Prandtl number such as protostellar disks and laboratory experiments.Comment: 5 pages, 6 figures, submitted to ApJ, changes made in response to referee repor

Multihop clustering algorithm for load balancing in wireless sensor networks

The paper presents a new cluster based routing algorithm that exploits the redundancy properties of the sensor networks in order to address the traditional problem of load balancing and energy efficiency in the WSNs.The algorithm makes use of the nodes in a sensor network of which area coverage is covered by the neighbours of the nodes and mark them as temporary cluster heads. The algorithm then forms two layers of multi hop communication. The bottom layer which involves intra cluster communication and the top layer which involves inter cluster communication involving the temporary cluster heads. Performance studies indicate that the proposed algorithm solves effectively the problem of load balancing and is also more efficient in terms of energy consumption from Leach and the enhanced version of Leach

Low-Rank Matrices on Graphs: Generalized Recovery & Applications

Many real world datasets subsume a linear or non-linear low-rank structure in a very low-dimensional space. Unfortunately, one often has very little or no information about the geometry of the space, resulting in a highly under-determined recovery problem. Under certain circumstances, state-of-the-art algorithms provide an exact recovery for linear low-rank structures but at the expense of highly inscalable algorithms which use nuclear norm. However, the case of non-linear structures remains unresolved. We revisit the problem of low-rank recovery from a totally different perspective, involving graphs which encode pairwise similarity between the data samples and features. Surprisingly, our analysis confirms that it is possible to recover many approximate linear and non-linear low-rank structures with recovery guarantees with a set of highly scalable and efficient algorithms. We call such data matrices as \textit{Low-Rank matrices on graphs} and show that many real world datasets satisfy this assumption approximately due to underlying stationarity. Our detailed theoretical and experimental analysis unveils the power of the simple, yet very novel recovery framework \textit{Fast Robust PCA on Graphs

Shearing box simulations in the Rayleigh unstable regime

We study the stability properties of Rayleigh unstable flows both in the purely hydrodynamic and magnetohydrodynamic (MHD) regimes for two different values of the shear $q=2.1, 4.2$ ($q = - d\ln\Omega / d\ln r$) and compare it with the Keplerian case $q=1.5$. We find that the $q>2$ regime is unstable both in the hydrodynamic and in the MHD limit (with an initially weak magnetic field). In this regime, the velocity fluctuations dominate the magnetic fluctuations. In contrast, in the $q<2$ (magnetorotational instability (MRI)) regime the magnetic fluctuations dominate. This highlights two different paths to MHD turbulence implied by the two regimes, suggesting that in the $q>2$ regime the instability produces primarily velocity fluctuations that cause magnetic fluctuations, with the causality reversed for the $q<2$ MRI unstable regime. We also find that the magnetic field correlation is increasingly localized as the shear is increased in the Rayleigh unstable regime. In calculating the time evolution of spatial averages of different terms in the MHD equations, we find that the $q>2$ regime is dominated by terms which are nonlinear in the fluctuations, whereas for $q<2$, the linear terms play a more significant role.Comment: accepted by MNRAS: 10 pages, 14 figures, 1 table; revised and expande