285 research outputs found
Effects of dust absorption on spectroscopic studies of turbulence
No full textInternational audienceWe study the effect of dust absorption on the recovery velocity and density spectra as well as on the anisotropies of magnetohydrodynamic turbulence using the velocity channel analysis (VCA), velocity coordinate spectrum (VCS) and velocity centroids. The dust limits volume up to an optical depth of unity. We show that in the case of the emissivity proportional to the density of emitters, the effects of random density get suppressed for strong dust absorption intensity variations arise from the velocity fluctuations only. However, for the emissivity proportional to squared density, both density and velocity fluctuations affect the observed intensities. We predict a new asymptotic regime for the spectrum of fluctuations for large scales exceeding the physical depths to unit optical depth. The spectrum gets shallower by unity in this regime. In addition, the dust absorption removes the degeneracy resulted in the universal K-3 spectrum of intensity fluctuations of self-absorbing medium reported by Lazarian & Pogosyan. We show that the predicted result is consistent with the available H II region emission data. We find that for sub-Alfvénic and trans-Alfvénic turbulence one can get the information about both the magnetic field direction and the fundamental Alfvén, fast and slow modes that constitute MHD turbulence
Extending velocity channel analysis for studying turbulence anisotropies
No full textInternational audienceWe extend the velocity channel analysis (VCA), introduced by Lazarian & Pogosyan, of the intensity fluctuations in the velocity slices of position-position-velocity (PPV) spectroscopic data from Doppler broadened lines to study statistical anisotropy of the underlying velocity and density that arises in a turbulent medium from the presence of magnetic field. In particular, we study analytically how the anisotropy of the intensity correlation in the channel maps changes with the thickness of velocity channels. In agreement with the earlier VCA studies, we find that the anisotropy in the thick channels reflects the anisotropy of the density field, while the relative contribution of density and velocity fluctuations to the thin velocity channels depends on the density spectral slope. We show that the anisotropies arising from Alfvén, slow and fast magnetohydrodynamical modes are different; in particular, the anisotropy in PPV created by fast modes is opposite to that created by Alfvén and slow modes, and this can be used to separate their contributions. We successfully compare our results with the recent numerical study of the PPV anisotropies measured with synthetic observations. We also extend our study to the medium with self-absorption as well as to the case of absorption lines. In addition, we demonstrate how the studies of anisotropy can be performed using interferometers
Models for Quadratic Algebras Associated with Second Order Superintegrable Systems in 2D
No full textThere are 13 equivalence classes of 2D second order quantum and classical superintegrable systems with nontrivial potential, each associated with a quadratic algebra of hidden symmetries. We study the finite and infinite irreducible representations of the quantum quadratic algebras though the construction of models in which the symmetries act on spaces of functions of a single complex variable via either differential operators or difference operators. In another paper we have already carried out parts of this analysis for the generic nondegenerate superintegrable system on the complex 2-sphere. Here we carry it out for a degenerate superintegrable system on the 2-sphere. We point out the connection between our results and a position dependent mass Hamiltonian studied by Quesne. We also show how to derive simple models of the classical quadratic algebras for superintegrable systems and then obtain the quantum models from the classical models, even though the classical and quantum quadratic algebras are distinct
The Kepler-Coulomb problem on SO(2, 2) hyperboloid
No full textIn this note the Kepler-Coulomb problem in hyperbolic space H2 2: z0 2 + z1 2 - z2 2 - z3 2 = R2 is discussed. � 2012 Pleiades Publishing, Ltd
Cloud forest dynamics in the mexican neotropics during the last 1300 years
No full textIn the present work, the problem of the motion of the classical particle in the Kepler-Coulomb field in three-dimensional hyperbolic space H 2 2: z 2 0 + z 2 1 - z 2 2 - z 2 3 = R 2 is solved in the framework of Hamilton-Jacobi equation. The requirements for the existence of bounded motion of particle are formulated. The equation of the trajectory of particle is obtained, and it is shown that all the finite trajectories are closed. It is also demonstrated that under the certain values (zero or negative) of the separation constant A the fall of the particle onto the center takes place. " 2013 Pleiades Publishing, Ltd.",,,,,,"10.1134/S1063778813090135",,,"http://hdl.handle.net/20.500.12104/40096","http://www.scopus.com/inward/record.url?eid=2-s2.0-84885830563&partnerID=40&md5=52f938ac91d5b20ba1a39a702f821b67",,,,,,"10",,"Physics of Atomic Nuclei",,"127
Classical Kepler-Coulomb problem on SO(2, 2) hyperboloid
No full textIn the present work, the problem of the motion of the classical particle in the Kepler-Coulomb field in three-dimensional hyperbolic space H 2 2: z 2 0 + z 2 1 - z 2 2 - z 2 3 = R 2 is solved in the framework of Hamilton-Jacobi equation. The requirements for the existence of bounded motion of particle are formulated. The equation of the trajectory of particle is obtained, and it is shown that all the finite trajectories are closed. It is also demonstrated that under the certain values (zero or negative) of the separation constant A the fall of the particle onto the center takes place. © 2013 Pleiades Publishing, Ltd
Structure Theory for Second Order 2D Superintegrable Systems with 1-Parameter Potentials
No full textThe structure theory for the quadratic algebra generated by first and second order constants of the motion for 2D second order superintegrable systems with nondegenerate (3-parameter) and or 2-parameter potentials is well understood, but the results for the strictly 1-parameter case have been incomplete. Here we work out this structure theory and prove that the quadratic algebra generated by first and second order constants of the motion for systems with 4 second order constants of the motion must close at order three with the functional relationship between the 4 generators of order four. We also show that every 1-parameter superintegrable system is Stäckel equivalent to a system on a constant curvature space
Laboratory experiments on the electrochemical remediation of the environment. Part 9: Microscale recovery of a soil metal pollutant and its extractant
No full textIn this paper, the Feynman path integral technique is applied for superintegrable potentials on two-dimensional spaces of nonconstant curvature: these spaces are Darboux spaces D I and D II. On D I, there are three, and on D II four such potentials. We are able to evaluate the path integral in most of the separating coordinate systems, leading to expressions for the Green functions, the discrete and continuous wave-functions, and the discrete energy-spectra. In some cases, however, the discrete spectrum cannot be stated explicitly, because it is either determined by a transcendental equation involving parabolic cylinder functions (Darboux space I), or by a higher order polynomial equation. The solutions on D I in particular show that superintegrable systems are not necessarily degenerate. We can also show how the limiting cases of flat space (constant curvature zero) and the two-dimensional hyperboloid (constant negative curvature) emerge. " Nauka/Interperiodica 2007.",,,,,,"10.1134/S1063779607030021",,,"http://hdl.handle.net/20.500.12104/43498","http://www.scopus.com/inward/record.url?eid=2-s2.0-34249935224&partnerID=40&md5=6657156137b432dc4fcf0095c04de515",,,,,,"3",,"Physics of Particles and Nuclei",,"29
Path integral approach for superintegrable potentials on spaces of non-constant curvature: II. Darboux spaces DIII and DIV
No full textThis is the second paper on the path integral approach of superintegrable systems on Darboux spaces, spaces of non-constant curvature. We analyze five and four superintegrable potentials in the spaces D III and D IV, respectively; these potentials were first given by Kalnins et al. We are able to evaluate the path integral in most of the separating coordinate systems, leading to expressions for the Green's functions, the discrete and continuous wavefunctions, and the discrete energy spectra. In some cases, however, the discrete spectrum cannot be stated explicitly because it is determined by a higher-order polynomial equation. We also show that the free motion in a Darboux space of type III can contain bound states, provided the boundary conditions are appropriate. We can state the corresponding energy spectrum and the wavefunctions. � 2007 Pleiades Publishing, Ltd
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