On the Role of Non-Periodic Orbits in The Semiclassical Quantization of the Truncated Hyperbola Billiard

Based on an accurate computation of the first 1851 quantal energy levels of the truncated hyperbola billiard, we have found an anomalous long-range modulation in the integrated level density. It is shown that the observed anomaly can be explained by an additional term in Gutzwiller's trace formula. This term is given as a sum over families of closed, non-periodic orbits which are reflected in a point of the billiard boundary where the boundary is continuously differentiable, but its curvature radius changes discontinuously.Comment: 8 pages, uu-encoded ps-fil

Particle-in-cell simulations of collisionless magnetic reconnection with a non-uniform guide field

Results are presented of a first study of collisionless magnetic reconnection starting from a recently found exact nonlinear force-free Vlasov–Maxwell equilibrium. The initial state has a Harris sheet magnetic field profile in one direction and a non-uniform guide field in a second direction, resulting in a spatially constant magnetic field strength as well as a constant initial plasma density and plasma pressure. It is found that the reconnection process initially resembles guide field reconnection, but that a gradual transition to anti-parallel reconnection happens as the system evolves. The time evolution of a number of plasma parameters is investigated, and the results are compared with simulations starting from a Harris sheet equilibrium and a Harris sheet plus constant guide field equilibrium

Discussion of a physical optics method and its application to absorbing smooth and slightly rough hexagonal prisms

Three different mathematical solutions of a physical optics model for far field diffraction by an aperture due to Karczewski and Wolf are discussed. Only one of them properly describes diffraction by an aperture and can, by applying Babinet's principle, be used to model diffraction by the corresponding plane obstacle, and by further approximation, diffraction by a particle. Studying absorbing scatterers allows a closer investigation of the external diffraction component because transmission is negligible. The physical optics model has been improved on two aspects: (i) To apply the diffraction model based on two-dimensional apertures more accurately to three-dimensional objects, a size parameter dependent volume obliquity factor is introduced, thus reducing the slightly overestimated side scattering computed for three-dimensional objects. (ii) To compensate simplifications in the underlying physical optics diffraction model for two-dimensional apertures [26] a size parameter dependent cross polarisation factor is implemented. It improves cross polarisation for diffraction and reflection by small particle facets. 2D patterns of P 11, –P 12/P 11 and P 22/P 11 and their azimuthal averages for slightly rough absorbing hexagonal prisms in fixed orientation are obtained and compared with results from the discrete dipole approximation. For particle orientations where shadowing is not negligible, improved phase functions are obtained by using a new method where the incident beam is divided into sub-beams with small triangular cross sections. The intersection points of the three sub-beam edges with the prism define the vertices of a triangle, which is treated by the beam tracer as an incidence-facing facet. This ensures that incident facing but shadowed crystal facets or regions thereof do not contribute to the phase functions. The method captures much of the fine detail contained in 2D scattering patterns obtained with DDA. This is important as speckle can be used for characterizing the size and roughness of small particles such as ice crystals.Peer reviewedFinal Accepted Versio

Modelling light scattering by absorbing smooth and slightly rough facetted particles

A method for approximating light scattering properties of strongly absorbing facetted particles which are large compared to the wavelength is presented. It consists in adding the approximated external diffraction and reflection far fields and is demonstrated for a smooth hexagonal prism. This computationally fast method is extended towards prisms with slightly rough surfaces by introducing a surface scaling factor in order to account for edge effects on subfacets forming the rough surface. These effects become more pronounced with decreasing subfacet dimension to wavelength ratio. Azimuthally resolved light scattering patterns, phase functions and degree of linear polarisation obtained by this method and by the Discrete Dipole Approximation are compared for hexagonal prisms with smooth and slightly rough surfaces, respectively.Peer reviewedSubmitted Versio

A Test of Social Disorganization on Juvenile Property and Violent Crime Rates by Zip Codes Within Two Nonmetropolitan Counties

This study tests the effects of social disorganization on juvenile crimes rates by zip code within two nonmetropolitan counties. It does so by examining the relationships between the selected social disorganization indicators of nontraditional family, residential mobility, and socioeconomic status (poverty) and violent and property crime among juveniles through the use of ANOVA testing. Secondary data obtained from the South Dakota Department of Corrections on adjudicated juveniles and their associated crime and residential location, as well as data from the United States Census Bureau is used and analyzed to test three main hypotheses. Findings indicate that areas characterized by poverty and residential mobility are associated with violent and property crime committed by juveniles. A discussion and implication section is provided

Neutral gas in Lyman-alpha emitting galaxies Haro 11 and ESO 338-IG04 measured through sodium absorption

Context. The Lyman alpha emission line of galaxies is an important tool for finding galaxies at high redshift, and thus probe the structure of the early universe. However, the resonance nature of the line and its sensitivity to dust and neutral gas is still not fully understood. Aims. We present measurements of the velocity, covering fraction and optical depth of neutral gas in front of two well known local blue compact galaxies that show Lyman alpha in emission: ESO 338-IG 04 and Haro 11. We thus test observationally the hypothesis that Lyman alpha can escape through neutral gas by being Doppler shifted out of resonance. Methods. We present integral field spectroscopy from the GIRAFFE/Argus spectrograph at VLT/FLAMES in Paranal, Chile. The excellent wavelength resolution allows us to accurately measure the velocity of the ionized and neutral gas through the H-alpha emission and Na D absorption, which traces the ionized medium and cold interstellar gas, respectively. We also present independent measurements with the VLT/X-shooter spectrograph which confirm our results. Results. For ESO 338-IG04, we measure no significant shift of neutral gas. The best fit velocity is -15 (16) km/s. For Haro 11, we see an outflow from knot B at 44 (13) km/s and infalling gas towards knot C with 32 (12) km/s. Based on the relative strength of the Na D absorption lines, we estimate low covering fractions of neutral gas (down to 10%) in all three cases. Conclusions. The Na D absorption likely occurs in dense clumps with higher column densities than where the bulk of the Ly-alpha scattering takes place. Still, we find no strong correlation between outflowing neutral gas and a high Lyman alpha escape fraction. The Lyman alpha photons from these two galaxies are therefore likely escaping due to a low column density and/or covering fraction.Comment: 9 pages, 3 figure

Incidence of rough and irregular atmospheric ice particles from Small Ice Detector 3 measurements

NERC, NE/E011225/1 © Author(s) 2013. This work is distributed under the Creative Commons Attribution 3.0 LicenseThe knowledge of properties of ice crystals such as size, shape, concavity and roughness is critical in the context of radiative properties of ice and mixed phase clouds. Limitations of current cloud probes to measure these properties can be circumvented by acquiring two-dimensional light scattering patterns instead of particle images. Such patterns were obtained in situ for the first time using the Small Ice Detector 3 (SID-3) probe during several flights in a variety of mid-latitude mixed phase and cirrus clouds. The patterns are analyzed using several measures of pattern texture, selected to reveal the magnitude of particle roughness or complexity. The retrieved roughness is compared to values obtained from a range of well-characterized test particles in the laboratory. It is found that typical in situ roughness corresponds to that found in the rougher subset of the test particles, and sometimes even extends beyond the most extreme values found in the laboratory. In this study we do not differentiate between small-scale, fine surface roughness and large-scale crystal complexity. Instead, we argue that both can have similar manifestations in terms of light scattering properties and also similar causes. Overall, the in situ data is consistent with ice particles with highly irregular or rough surfaces being dominant. Similar magnitudes of roughness were found in growth and sublimation zones of cirrus. The roughness was found to be negatively correlated with the halo ratio, but not with other thermodynamic or microphysical properties found in situ. Slightly higher roughness was observed in cirrus forming in clean oceanic airmasses than in a continental, polluted one. Overall, the roughness and complexity is expected to lead to increased shortwave cloud reflectivity, in comparison with cirrus composed of more regular, smooth ice crystal shapes. These findings put into question suggestions that climate could be modified through aerosol seeding to reduce cirrus cover and optical depth, as the seeding may result in decreased shortwave reflectivity.Peer reviewe

Conjugacy in Baumslag's group, generic case complexity, and division in power circuits

The conjugacy problem belongs to algorithmic group theory. It is the following question: given two words x, y over generators of a fixed group G, decide whether x and y are conjugated, i.e., whether there exists some z such that zxz^{-1} = y in G. The conjugacy problem is more difficult than the word problem, in general. We investigate the complexity of the conjugacy problem for two prominent groups: the Baumslag-Solitar group BS(1,2) and the Baumslag(-Gersten) group G(1,2). The conjugacy problem in BS(1,2) is TC^0-complete. To the best of our knowledge BS(1,2) is the first natural infinite non-commutative group where such a precise and low complexity is shown. The Baumslag group G(1,2) is an HNN-extension of BS(1,2). We show that the conjugacy problem is decidable (which has been known before); but our results go far beyond decidability. In particular, we are able to show that conjugacy in G(1,2) can be solved in polynomial time in a strongly generic setting. This means that essentially for all inputs conjugacy in G(1,2) can be decided efficiently. In contrast, we show that under a plausible assumption the average case complexity of the same problem is non-elementary. Moreover, we provide a lower bound for the conjugacy problem in G(1,2) by reducing the division problem in power circuits to the conjugacy problem in G(1,2). The complexity of the division problem in power circuits is an open and interesting problem in integer arithmetic.Comment: Section 5 added: We show that an HNN extension G = < H, b | bab^-1 = {\phi}(a), a \in A > has a non-amenable Schreier graph with respect to the base group H if and only if A \neq H \neq

Physics of Reconnection and MMS Mission

Reconnection is the most important process driving the Earth's magnetosphere. Key to the success of the MMS science plan is the coupling of theory and observation. Determining the kinetic processes occurring in the diffusion region and physical parameters that control the rate of magnetic reconnection are among primary objectives of the MMS mission. Analysis of the role played by particle inertial effects in the diffusion region where the plasma is unmagnetized will be presented. The reconnection electric field in he diffusion region is supported primarily by particle non-gyrotropic effects. At the quasi-steady stage the reconnection electric field serves to accelerate and heat the incoming plasma population to maintain the current flow in the diffusion region the pressure balance. The primary mechanism controlling the dissipation in the vicinity of the reconnection site is incorporated into the fluid description in terms of non-gyrotropic corrections to the. induction and energy equations. The results of kinetic and fluid simulations illustrating the physics of magnetic reconnection will be presented. We will dem~:tistrate that kinetic nongyrotropic effects can significantly alter the global magnetosphere evolution and location of reconnection sites