On the 3-D structure and dissipation of reconnection-driven flow-bursts

The structure of magnetic reconnection-driven outflows and their dissipation are explored with large-scale, 3-D particle-in-cell (PIC) simulations. Outflow jets resulting from 3-D reconnection with a finite length x-line form fronts as they propagate into the downstream medium. A large pressure increase ahead of this ``reconnection jet front'' (RJF), due to reflected and transmitted ions, slows the front so that its velocity is well below the velocity of the ambient ions in the core of the jet. As a result, the RJF slows and diverts the high-speed flow into the direction perpendicular to the reconnection plane. The consequence is that the RJF acts as a thermalization site for the ion bulk flow and contributes significantly to the dissipation of magnetic energy during reconnection even though the outflow jet is subsonic. This behavior has no counterpart in 2-D reconnection. A simple analytic model predicts the front velocity and the fraction of the ion bulk flow energy that is dissipated

Racing Multi-Objective Selection Probabilities

In the context of Noisy Multi-Objective Optimization, dealing with uncertainties requires the decision maker to define some preferences about how to handle them, through some statistics (e.g., mean, median) to be used to evaluate the qualities of the solutions, and define the corresponding Pareto set. Approximating these statistics requires repeated samplings of the population, drastically increasing the overall computational cost. To tackle this issue, this paper proposes to directly estimate the probability of each individual to be selected, using some Hoeffding races to dynamically assign the estimation budget during the selection step. The proposed racing approach is validated against static budget approaches with NSGA-II on noisy versions of the ZDT benchmark functions

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Linear response within the projection-based renormalization method: Many-body corrections beyond the random phase approximation

The explicit evaluation of linear response coefficients for interacting many-particle systems still poses a considerable challenge to theoreticians. In this work we use a novel many-particle renormalization technique, the so-called projector-based renormalization method, to show how such coefficients can systematically be evaluated. To demonstrate the prospects and power of our approach we consider the dynamical wave-vector dependent spin susceptibility of the two-dimensional Hubbard model and also determine the subsequent magnetic phase diagram close to half-filling. We show that the superior treatment of (Coulomb) correlation and fluctuation effects within the projector-based renormalization method significantly improves the standard random phase approximation results.Comment: 17 pages, 7 figures, revised versio

Kinetic signatures of the region surrounding the X-line in asymmetric (magnetopause) reconnection

Kinetic particle-in-cell simulations are used to identify signatures of the electron diffusion region (EDR) and its surroundings during asymmetric magnetic reconnection. A "shoulder" in the sunward pointing normal electric field (EN > 0) at the reconnection magnetic field reversal is a good indicator of the EDR, and is caused by magnetosheath electron meandering orbits in the vicinity of the x-line. Earthward of the X-line, electrons accelerated by EN form strong currents and crescent-shaped distribution functions in the plane perpendicular to B. Just downstream of the X-line, parallel electric fields create field-aligned crescent electron distribution functions. In the immediate upstream magnetosheath, magnetic field strength, plasma density, and perpendicular electron temperatures are lower than the asymptotic state. In the magnetosphere inflow region, magnetosheath ions intrude resulting in an Earthward pointing electric field and parallel heating of magnetospheric particles. Many of the above properties persist with a guide field of at least unity.Comment: Submitted to Geophysical Research Letter

Temperature dependent graphene suspension due to thermal Casimir interaction

Thermal effects contributing to the Casimir interaction between objects are usually small at room temperature and they are difficult to separate from quantum mechanical contributions at higher temperatures. We propose that the thermal Casimir force effect can be observed for a graphene flake suspended in a fluid between substrates at the room temperature regime. The properly chosen materials for the substrates and fluid induce a Casimir repulsion. The balance with the other forces, such as gravity and buoyancy, results in a stable temperature dependent equilibrium separation. The suspended graphene is a promising system due to its potential for observing thermal Casimir effects at room temperature.Comment: 5 pages, 4 figures, in APL production 201

On the Cause of Supra-Arcade Downflows in Solar Flares

A model of supra-arcade downflows (SADs), dark low density regions also known as tadpoles that propagate sunward during solar flares, is presented. It is argued that the regions of low density are flow channels carved by sunward-directed outflow jets from reconnection. The solar corona is stratified, so the flare site is populated by a lower density plasma than that in the underlying arcade. As the jets penetrate the arcade, they carve out regions of depleted plasma density which appear as SADs. The present interpretation differs from previous models in that reconnection is localized in space but not in time. Reconnection is continuous in time to explain why SADs are not filled in from behind as they would if they were caused by isolated descending flux tubes or the wakes behind them due to temporally bursty reconnection. Reconnection is localized in space because outflow jets in standard two-dimensional reconnection models expand in the normal (inflow) direction with distance from the reconnection site, which would not produce thin SADs as seen in observations. On the contrary, outflow jets in spatially localized three-dimensional reconnection with an out-of-plane (guide) magnetic field expand primarily in the out-of-plane direction and remain collimated in the normal direction, which is consistent with observed SADs being thin. Two-dimensional proof-of-principle simulations of reconnection with an out-of-plane (guide) magnetic field confirm the creation of SAD-like depletion regions and the necessity of density stratification. Three-dimensional simulations confirm that localized reconnection remains collimated.Comment: 16 pages, 5 figures, accepted to Astrophysical Journal Letters in August, 2013. This version is the accepted versio