Three charged particles in the continuum. Astrophysical examples

We suggest a new adiabatic approach for description of three charged particles in the continuum. This approach is based on the Coulomb-Fourier transformation (CFT) of three body Hamiltonian, which allows to develop a scheme, alternative to Born-Oppenheimer one. The approach appears as an expansion of the kernels of corresponding integral transformations in terms of small mass-ratio parameter. To be specific, the results are presented for the system $ppe$ in the continuum. The wave function of a such system is compared with that one which is used for estimation of the rate for triple reaction $p+p+e\to d+\nu,$ which take place as a step of $pp$-cycle in the center of the Sun. The problem of microscopic screening for this particular reaction is discussed

Stereo Computation for a Single Mixture Image

This paper proposes an original problem of \emph{stereo computation from a single mixture image}-- a challenging problem that had not been researched before. The goal is to separate (\ie, unmix) a single mixture image into two constitute image layers, such that the two layers form a left-right stereo image pair, from which a valid disparity map can be recovered. This is a severely illposed problem, from one input image one effectively aims to recover three (\ie, left image, right image and a disparity map). In this work we give a novel deep-learning based solution, by jointly solving the two subtasks of image layer separation as well as stereo matching. Training our deep net is a simple task, as it does not need to have disparity maps. Extensive experiments demonstrate the efficacy of our method.Comment: Accepted by European Conference on Computer Vision (ECCV) 201

A survey of spinning test particle orbits in Kerr spacetime

We investigate the dynamics of the Papapetrou equations in Kerr spacetime. These equations provide a model for the motion of a relativistic spinning test particle orbiting a rotating (Kerr) black hole. We perform a thorough parameter space search for signs of chaotic dynamics by calculating the Lyapunov exponents for a large variety of initial conditions. We find that the Papapetrou equations admit many chaotic solutions, with the strongest chaos occurring in the case of eccentric orbits with pericenters close to the limit of stability against plunge into a maximally spinning Kerr black hole. Despite the presence of these chaotic solutions, we show that physically realistic solutions to the Papapetrou equations are not chaotic; in all cases, the chaotic solutions either do not correspond to realistic astrophysical systems, or involve a breakdown of the test-particle approximation leading to the Papapetrou equations (or both). As a result, the gravitational radiation from bodies spiraling into much more massive black holes (as detectable, for example, by LISA, the Laser Interferometer Space Antenna) should not exhibit any signs of chaos.Comment: Submitted to Phys. Rev. D. Follow-up to gr-qc/0210042. Figures are low-resolution in order to satisfy archive size constraints; a high-resolution version is available at http://www.michaelhartl.com/papers

Channel-Independent and Sensor-Independent Stimulus Representations

This paper shows how a machine, which observes stimuli through an uncharacterized, uncalibrated channel and sensor, can glean machine-independent information (i.e., channel- and sensor-independent information) about the stimuli. First, we demonstrate that a machine defines a specific coordinate system on the stimulus state space, with the nature of that coordinate system depending on the device's channel and sensor. Thus, machines with different channels and sensors "see" the same stimulus trajectory through state space, but in different machine-specific coordinate systems. For a large variety of physical stimuli, statistical properties of that trajectory endow the stimulus configuration space with differential geometric structure (a metric and parallel transfer procedure), which can then be used to represent relative stimulus configurations in a coordinate-system-independent manner (and, therefore, in a channel- and sensor-independent manner). The resulting description is an "inner" property of the stimulus time series in the sense that it does not depend on extrinsic factors like the observer's choice of a coordinate system in which the stimulus is viewed (i.e., the observer's choice of channel and sensor). This methodology is illustrated with analytic examples and with a numerically simulated experiment. In an intelligent sensory device, this kind of representation "engine" could function as a "front-end" that passes channel/sensor-independent stimulus representations to a pattern recognition module. After a pattern recognizer has been trained in one of these devices, it could be used without change in other devices having different channels and sensors.Comment: The results of a numerically simulated experiment, which illustrates the proposed method, have been added to the version submitted on October 27, 2004. This paper has been accepted for publication in the Journal of Applied Physics. For related papers, see http://www.geocities.com/dlevin2001

The non-self-adjointness of the radial momentum operator in n dimensions

The non self-adjointness of the radial momentum operator has been noted before by several authors, but the various proofs are incorrect. We give a rigorous proof that the $n$-dimensional radial momentum operator is not self- adjoint and has no self-adjoint extensions. The main idea of the proof is to show that this operator is unitarily equivalent to the momentum operator on $L^{2}[(0,\infty),dr]$ which is not self-adjoint and has no self-adjoint extensions.Comment: Some text and a reference adde

Formation of “Red Scare” Concept in USA in First Half of XX Century

The issue of how the an important and multifaceted aspect of domestic and foreign policy formed by US FBI, called the "Red Scare" is addressed in the article. It is shown that this political and ideological concept seemed unacceptable for distribution in the United States, since it created a danger of the penetration of communist ideas and their adherents into all government bodies and major public organizations. Factors that influenced the strengthening of the FBI’s position in the fight against communist ideology in the United States in the 1920s, in particular, terrorist acts carried out by left-wing forces, which allowed the FBI to implement a program of struggle (Palmer raids) with organizations, adhering to communist views are examined. The measures taken by the FBI and its director John Edgar Hoover in the 1930s against Soviet intelligence, which contributed to reinforcing negative perceptions of the “Red Scare” within the agency are highlighted. The authors conclude that the position of the FBI influenced the building of the attitude of the entire US intelligence community in this vein, which in turn had a great impact on the development of the country’s domestic and foreign policy