1,975 research outputs found
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 -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
Impulsive feedback control for dosing applications
This paper addresses a design procedure of pulse-modulated feedback control
solving a dosing problem defined for implementation in a manual mode. Discrete
dosing, as a control strategy, is characterized by exerting control action on
the plant in impulsive manner at certain time instants. Dosing applications
appear primarily in chemical industry and medicine where the control signal
constitutes a sequence of (chemically or pharmacologically) active substance
quantities (doses) administered to achieve a desired result. When the doses and
the instants of their administration are adjusted as functions of some measured
variable, a feedback control loop exhibiting nonlinear dynamics arises. The
impulsive character of the interaction between the controller and the plant
makes the resulting closed-loop system non-smooth. Limitations of the control
law with respect to control goals are discussed. An application of the approach
at hand to neuromuscular blockade in closed-loop anesthesia is considered in a
numerical example
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