Theory of "Jitter" Radiation from Small-Scale Random Magnetic Fields and Prompt Emission from Gamma-Ray Burst Shocks

Abridged.-- We demonstrate that the radiation emitted by ultrarelativistic electrons in highly nonuniform, small-scale magnetic fields is different from synchrotron radiation if the electron's transverse deflections in these fields are much smaller than the beaming angle. A quantitative analytical theory of this radiation, which we refer to as jitter radiation, is developed. It is shown that the emergent spectrum is determined by statistical properties of the magnetic field. As an example,we then use the model of a magnetic field in internal shocks of GRBs. The spectral power distribution of radiation produced by the power-law electrons is well described by a sharply broken power-law with indices 1 and -(p-1)/2 and the jitter break frequency is independent of the field strength but depends on the electron density in the ejecta. Since large-scale fields may also be present in the ejecta, we construct a two-component, jitter+synchrotron spectral model of the prompt $\gamma$-ray emission. Quite surprisingly, this model seems to be readily capable of explaining several properties of time-resolved spectra of some GRBs, such as (i) the violation of the constraint on the low-energy spectral index called the synchrotron ``line of death'', (ii) the sharp spectral break at the peak frequency, inconsistent with the broad synchrotron bump, (iii) the evidence for two spectral sub-components, and (iv) possible existence of emission features called ``GRB lines''. We believe these facts strongly support both the existence of small-scale magnetic fields and the proposed radiation mechanism from GRB shocks. As an example, we use the composite model to analyze GRB 910503 which has two spectral peaks.Comment: 12 pages (emulateapj), 11 figures (EPS), ApJ, accepted. For related work, see http://cfa-www.harvard.edu/~mmedved

Interstellar Scintillations of Polarization of Compact Sources

We demostrate that the measurement of fluctuations of polarization due to the galactic interstellar scintillations may be used to study the structure of the radiation field at compact radio sources. We develop a mathematical formalism and demonstrate it on a simple analytical model in which the scale of the polarization variation through the source is comparable to the source size. The predicted amplitude of modulation of the polarized radiation flux is ~20% x (pi_s) x (m_sc), where (pi_s) is the characteristic degree of polarization of radiation at the source and (m_sc) is the typical modulation index due to scattering, i.e., (m_sc)~1 for diffractive scintillations and (m_sc)<1 for refractive scintillations.Comment: 5 pages, 2 figures, emilateapj.sty. Submitted to ApJ

MEMS-Based Terahertz Photoacoustic Chemical Sensing System

Advancements in microelectromechanical system (MEMS) technology over the last several decades has been a driving force behind miniaturizing and improving sensor designs. In this work, a specialized cantilever pressure sensor was designed, modeled, and fabricated to investigate the photoacoustic (PA) response of gases to terahertz (THz) radiation under low-vacuum conditions associated with high-resolution spectroscopy. Microfabricated cantilever devices made using silicon-on-insulator (SOI) wafers were tested in a custom-built test chamber in this first ever demonstration of a cantilever-based PA chemical sensor and spectroscopy system in the THz frequency regime. The THz radiation source was amplitude modulated to excite acoustic waves in the chamber, and PA molecular spectroscopy of a gas species was performed. An optical measurement technique was used to evaluate the PA effect on the cantilever sensor; a laser beam was reflected off the cantilever tip and through an iris to a photodiode. As the cantilever movement deflected the laser beam, the beam was clipped by an iris and generated the PA signal. Experimental data indicated a predominantly linear response in signal amplitude from the photodiode measurement technique, which directly correlated to measured cantilever deflections. Using the custom-designed PA chamber and MEMS cantilever sensor, excellent low-pressure PA spectral data of methyl cyanide (CH3CN) at 2 to 40 mTorr range has been obtained. At low chamber pressures, the sensitivity of our system was 1.97 × 10−5 cm−1 and had an excellent normalized noise equivalent absorption (NNEA) coefficient of 1.39 × 10−9 cm−1 W Hz-½ using a 0.5 s signal averaging time

Chaos-Order Transition in Matrix Theory

Classical dynamics in SU(2) Matrix theory is investigated. A classical chaos-order transition is found. For the angular momentum small enough (even for small coupling constant) the system exhibits a chaotic behavior, for angular momentum large enough the system is regular.Comment: 14 pages, Latex, 10 figure

Terahertz Photoacoustic Spectroscopy Using an MEMS Cantilever Sensor

In this paper, a microelectromechanical systems cantilever sensor was designed, modeled, and fabricated to measure the photoacoustic (PA) response of gases under very low vacuum conditions. The micromachined devices were fabricated using silicon-on-insulator wafers and then tested in a custom-built, miniature, vacuum chamber during this first-ever demonstration. Terahertz radiation was amplitude modulated to excite the gas under test and perform PA molecular spectroscopy. Experimental data show a predominantly linear response that directly correlates measured cantilever deflection to PA signals. Excellent low pressure (i.e., 2-40 mTorr) methyl cyanide PA spectral data were collected resulting in a system sensitivity of 1.97 × 10 -5 cm -1 and a normalized noise equivalent absorption coefficient of 1.39 × 10 -9 cm -1 W Hz -1/2

Classification of online toxic comments using the logistic regression and neural networks models

The paper addresses the questions of abusive content identification in the Internet. It is presented the solving of the task of toxic online comments classification, which was issued on the site of machine learning Kaggle (www.Kaggle.com) in March of 2018. Based on the analysis of initial data, four models for solving the task are proposed: logistic regression model and three neural networks models - convolutional neural network (Conv), long shortterm memory (LSTM), and Conv + LSTM. All models are realized as a program in Python 3, which has simple structure and can be adapted to solve other tasks. The results of the classification problem solving with help of proposed models are presented. It is concluded that all models provide successful solving of the task, but the combined model Conv + LSTM is the most effective, so as it provides the best accuracy. © 2018 Author(s)

The geometry of spontaneous spiking in neuronal networks

The mathematical theory of pattern formation in electrically coupled networks of excitable neurons forced by small noise is presented in this work. Using the Freidlin-Wentzell large deviation theory for randomly perturbed dynamical systems and the elements of the algebraic graph theory, we identify and analyze the main regimes in the network dynamics in terms of the key control parameters: excitability, coupling strength, and network topology. The analysis reveals the geometry of spontaneous dynamics in electrically coupled network. Specifically, we show that the location of the minima of a certain continuous function on the surface of the unit n-cube encodes the most likely activity patterns generated by the network. By studying how the minima of this function evolve under the variation of the coupling strength, we describe the principal transformations in the network dynamics. The minimization problem is also used for the quantitative description of the main dynamical regimes and transitions between them. In particular, for the weak and strong coupling regimes, we present asymptotic formulas for the network activity rate as a function of the coupling strength and the degree of the network. The variational analysis is complemented by the stability analysis of the synchronous state in the strong coupling regime. The stability estimates reveal the contribution of the network connectivity and the properties of the cycle subspace associated with the graph of the network to its synchronization properties. This work is motivated by the experimental and modeling studies of the ensemble of neurons in the Locus Coeruleus, a nucleus in the brainstem involved in the regulation of cognitive performance and behavior

Towards a Simple Model of Compressible Alfvenic Turbulence

A simple model collisionless, dissipative, compressible MHD (Alfvenic) turbulence in a magnetized system is investigated. In contrast to more familiar paradigms of turbulence, dissipation arises from Landau damping, enters via nonlinearity, and is distributed over all scales. The theory predicts that two different regimes or phases of turbulence are possible, depending on the ratio of steepening to damping coefficient (m_1/m_2). For strong damping (|m_1/m_2|<1), a regime of smooth, hydrodynamic turbulence is predicted. For |m_1/m_2|>1, steady state turbulence does not exist in the hydrodynamic limit. Rather, spikey, small scale structure is predicted.Comment: 6 pages, one figure, REVTeX; this version to be published in PRE. For related papers, see http://sdphpd.ucsd.edu/~medvedev/papers.htm