Numerical Studies of Weakly Stochastic Magnetic Reconnection

We study the effects of turbulence on magnetic reconnection using three-dimensional numerical simulations. This is the first attempt to test a model of fast magnetic reconnection proposed by Lazarian & Vishniac (1999), which assumes the presence of weak, small-scale magnetic field structure near the current sheet. This affects the rate of reconnection by reducing the transverse scale for reconnection flows and by allowing many independent flux reconnection events to occur simultaneously. We performed a number of simulations to test the dependencies of the reconnection speed, defined as the ratio of the inflow velocity to the Alfven speed, on the turbulence power, the injection scale and resistivity. Our results show that turbulence significantly affects the topology of magnetic field near the diffusion region and increases the thickness of the outflow region. We confirm the predictions of the Lazarian & Vishniac model. In particular, we report the growth of the reconnection speed proportional to ~ V^2, where V is the amplitude of velocity at the injection scale. It depends on the injection scale l as ~ (l/L)^(2/3), where L is the size of the system, which is somewhat faster but still roughly consistent with the theoretical expectations. We also show that for 3D reconnection the Ohmic resistivity is important in the local reconnection events only, and the global reconnection rate in the presence of turbulence does not depend on it.Comment: 8 pages, 8 figure

The role of pressure anisotropy in the turbulent intracluster medium

In low-density plasma environments, such as the intracluster medium (ICM), the Larmour frequency is much larger than the ion-ion collision frequency. In such a case, the thermal pressure becomes anisotropic with respect to the magnetic field orientation and the evolution of the turbulent gas is more correctly described by a kinetic approach. A possible description of these collisionless scenarios is given by the so-called kinetic magnetohydrodynamic (KMHD) formalism, in which particles freely stream along the field lines, while moving with the field lines in the perpendicular direction. In this way a fluid-like behavior in the perpendicular plane is restored. In this work, we study fast growing magnetic fluctuations in the smallest scales which operate in the collisionless plasma that fills the ICM. In particular, we focus on the impact of a particular evolution of the pressure anisotropy and its implications for the turbulent dynamics of observables under the conditions prevailing in the ICM. We present results from numerical simulations and compare the results which those obtained using an MHD formalism.Comment: 7 pages, 14 figures, Journal of Physics: Conference Serie

Reconnection Studies Under Different Types of Turbulence Driving

We study a model of fast magnetic reconnection in the presence of weak turbulence proposed by Lazarian and Vishniac (1999) using three-dimensional direct numerical simulations. The model has been already successfully tested in Kowal et al. (2009) confirming the dependencies of the reconnection speed $V_{rec}$ on the turbulence injection power $P_{inj}$ and the injection scale $l_{inj}$ expressed by a constraint $V_{rec} \sim P_{inj}^{1/2} l_{inj}^{3/4}$ and no observed dependency on Ohmic resistivity. In Kowal et al. (2009), in order to drive turbulence, we injected velocity fluctuations in Fourier space with frequencies concentrated around $k_{inj}=1/l_{inj}$, as described in Alvelius (1999). In this paper we extend our previous studies by comparing fast magnetic reconnection under different mechanisms of turbulence injection by introducing a new way of turbulence driving. The new method injects velocity or magnetic eddies with a specified amplitude and scale in random locations directly in real space. We provide exact relations between the eddy parameters and turbulent power and injection scale. We performed simulations with new forcing in order to study turbulent power and injection scale dependencies. The results show no discrepancy between models with two different methods of turbulence driving exposing the same scalings in both cases. This is in agreement with the Lazarian and Vishniac (1999) predictions. In addition, we performed a series of models with varying viscosity $\nu$. Although Lazarian and Vishniac (1999) do not provide any prediction for this dependence, we report a weak relation between the reconnection speed with viscosity, $V_{rec}\sim\nu^{-1/4}$.Comment: 19 pages, 9 figures. arXiv admin note: text overlap with arXiv:0903.205

Mechanical System Reliability and Cost Integration Using a Sequential Linear Approximation Method

The development of new products is dependent on product designs that incorporate high levels of reliability along with a design that meets predetermined levels of system cost. Additional constraints on the product include explicit and implicit performance requirements. Existing reliability and cost prediction methods result in no direct linkage between variables affecting these two dominant product attributes. A methodology to integrate reliability and cost estimates using a sequential linear approximation method is proposed. The sequential linear approximation method utilizes probability of failure sensitivities determined from probabilistic reliability methods as well a manufacturing cost sensitivities. The application of the sequential linear approximation method to a mechanical system is demonstrated

Mechanical system reliability for long life space systems

The creation of a compendium of mechanical limit states was undertaken in order to provide a reference base for the application of first-order reliability methods to mechanical systems in the context of the development of a system level design methodology. The compendium was conceived as a reference source specific to the problem of developing the noted design methodology, and not an exhaustive or exclusive compilation of mechanical limit states. The compendium is not intended to be a handbook of mechanical limit states for general use. The compendium provides a diverse set of limit-state relationships for use in demonstrating the application of probabilistic reliability methods to mechanical systems. The compendium is to be used in the reliability analysis of moderately complex mechanical systems

Two-Stage Convolutional Neural Network for Breast Cancer Histology Image Classification

This paper explores the problem of breast tissue classification of microscopy images. Based on the predominant cancer type the goal is to classify images into four categories of normal, benign, in situ carcinoma, and invasive carcinoma. Given a suitable training dataset, we utilize deep learning techniques to address the classification problem. Due to the large size of each image in the training dataset, we propose a patch-based technique which consists of two consecutive convolutional neural networks. The first "patch-wise" network acts as an auto-encoder that extracts the most salient features of image patches while the second "image-wise" network performs classification of the whole image. The first network is pre-trained and aimed at extracting local information while the second network obtains global information of an input image. We trained the networks using the ICIAR 2018 grand challenge on BreAst Cancer Histology (BACH) dataset. The proposed method yields 95 % accuracy on the validation set compared to previously reported 77 % accuracy rates in the literature. Our code is publicly available at https://github.com/ImagingLab/ICIAR2018Comment: 10 pages, 5 figures, ICIAR 2018 conferenc