Extracting 3D parametric curves from 2D images of Helical objects

Helical objects occur in medicine, biology, cosmetics, nanotechnology, and engineering. Extracting a 3D parametric curve from a 2D image of a helical object has many practical applications, in particular being able to extract metrics such as tortuosity, frequency, and pitch. We present a method that is able to straighten the image object and derive a robust 3D helical curve from peaks in the object boundary. The algorithm has a small number of stable parameters that require little tuning, and the curve is validated against both synthetic and real-world data. The results show that the extracted 3D curve comes within close Hausdorff distance to the ground truth, and has near identical tortuosity for helical objects with a circular profile. Parameter insensitivity and robustness against high levels of image noise are demonstrated thoroughly and quantitatively

Suitably graded THB-spline refinement and coarsening: Towards an adaptive isogeometric analysis of additive manufacturing processes

In the present work we introduce a complete set of algorithms to efficiently perform adaptive refinement and coarsening by exploiting truncated hierarchical B-splines (THB-splines) defined on suitably graded isogeometric meshes, that are called admissible mesh configurations. We apply the proposed algorithms to two-dimensional linear heat transfer problems with localized moving heat source, as simplified models for additive manufacturing applications. We first verify the accuracy of the admissible adaptive scheme with respect to an overkilled solution, for then comparing our results with similar schemes which consider different refinement and coarsening algorithms, with or without taking into account grading parameters. This study shows that the THB-spline admissible solution delivers an optimal discretization for what concerns not only the accuracy of the approximation, but also the (reduced) number of degrees of freedom per time step. In the last example we investigate the capability of the algorithms to approximate the thermal history of the problem for a more complicated source path. The comparison with uniform and non-admissible hierarchical meshes demonstrates that also in this case our adaptive scheme returns the desired accuracy while strongly improving the computational efficiency.Comment: 20 pages, 12 figure

The Structure and Dynamical Evolution of Dark Matter Halos

(Shortened) We use N-body simulations to investigate the structure and dynamical evolution of dark matter halos in galaxy clusters. Our sample consists of nine massive halos from an EdS universe with scale free power spectrum and n = -1. Halos are resolved by ~20000 particles each, with a dynamical resolution of 20-25 kpc. Large scale tidal fields are included up to L=150 Mpc using background particles. The halo formation process can be characterized by the alternation of two dynamical configurations: a merging phase and a relaxation phase, defined by their signature on the evolution of the total mass and rms velocity. Halos spend on average one 1/3 of their evolution in the merging phase and 2/3 in the relaxation phase. Using this definition, we study the density profiles and their change during the halo history. The average density profiles are fitted by the NFW analytical model with an rms residual of 17% between the virial radius Rv and 0.01 Rv. The Hernquist (1990) profiles fits the same halos with an rms residual of 26%. The trend with mass of the scale radius of these fits is marginally consistent with that found by Cole & Lacey (1996): in comparison our halos are more centrally concentrated, and the relation between scale radius and halo mass is slightly steeper. We find a moderately large scatter in this relation, due both to dynamical evolution within halos and to fluctuations in the halo population. We analyze the dynamical equilibrium of our halos using the Jeans' equation, and find that on average they are approximately in equilibrium within their virial radius. Finally, we find that the projected mass profiles of our simulated halos are in very good agreement with the profiles of three rich galaxy clusters derived from strong and weak gravitational lensing observations.Comment: 20 pages, Latex, with all figures included. Modified to match the published versio

The Genesis of an Impulsive Coronal Mass Ejection observed at Ultra-High Cadence by AIA on SDO

The study of fast, eruptive events in the low solar corona is one of the science objectives of the Atmospheric Imaging Assembly (AIA) imagers on the recently launched Solar Dynamics Observatory (SDO), which take full disk images in ten wavelengths with arcsecond resolution and 12 sec cadence. We study with AIA the formation of an impulsive coronal mass ejection (CME) which occurred on June 13, 2010 and was associated with an M1.0 class flare. Specifically, we analyze the formation of the CME EUV bubble and its initial dynamics and thermal evolution in the low corona using AIA images in three wavelengths (171, 193 and 211 A). We derive the first ultra-high cadence measurements of the temporal evolution of the CME bubble aspect ratio (=bubble-height/bubble-radius). Our main result is that the CME formation undergoes three phases: it starts with a slow self-similar expansion followed by a fast but short-lived (~ 70 sec) period of strong lateral over-expansion which essentially creates the CME. Then the CME undergoes another phase of self-similar expansion until it exits the AIA field of view. During the studied interval, the CME height-time profile shows a strong, short-lived, acceleration followed by deceleration. The lateral overexpansion phase coincides with the deceleration phase. The impulsive flare heating and CME acceleration are closely coupled. However, the lateral overexpansion of the CME occurs during the declining phase and is therefore not linked to flare reconnection. In addition, the multi-thermal analysis of the bubble does not show significant evidence of temperature change.Comment: 2010 in pres

Density Waves Inside Inner Lindblad Resonance: Nuclear Spirals in Disk Galaxies

We analyze formation of grand-design two-arm spiral structure in the nuclear regions of disk galaxies. Such morphology has been recently detected in a number of objects using high-resolution near-infrared observations. Motivated by the observed (1) continuity between the nuclear and kpc-scale spiral structures, and by (2) low arm-interarm contrast, we apply the density wave theory to explain the basic properties of the spiral nuclear morphology. In particular, we address the mechanism for the formation, maintenance and the detailed shape of nuclear spirals. We find, that the latter depends mostly on the shape of the underlying gravitational potential and the sound speed in the gas. Detection of nuclear spiral arms provides diagnostics of mass distribution within the central kpc of disk galaxies. Our results are supported by 2D numerical simulations of gas response to the background gravitational potential of a barred stellar disk. We investigate the parameter space allowed for the formation of nuclear spirals using a new method for constructing a gravitational potential in a barred galaxy, where positions of resonances are prescribed.Comment: 18 pages, 9 figures, higher resolution available at http://www.pa.uky.edu/~ppe/papers/nucsp.ps.g

Dynamical friction and the evolution of satellites in virialized halos: the theory of linear response

The evolution of a small satellite inside a more massive truncated isothermal spherical halo is studied using both the Theory of Linear Response for dynamical friction and N-Body simulations. The analytical approach includes the effects of the gravitational wake, of the tidal deformation and the shift of the barycenter of the primary, so unifying the local versus global interpretation of dynamical friction. Sizes, masses, orbital energies and eccentricities are chosen as expected in hierarchical clustering models. We find that in general the drag force in self-gravitating backgrounds is weaker than in uniform media and that the orbital decay is not accompanied by a significant circularization. We also show that the dynamical friction time scale is weakly dependent on the initial circularity. We provide a fitting formula for the decay time that includes the effect of mass and angular momentum loss. Live satellites with dense cores can survive disruption up to an Hubble time within the primary, notwithstanding the initial choice of orbital parameters. Dwarf spheroidal satellites of the Milky Way, like Sagittarius A and Fornax, have already suffered mass stripping and, with their present masses, the sinking times exceed 10 Gyr even if they are on very eccentric orbits.Comment: 27 pages including 9 figures. Accepted for publication in the Astrophysical Journal. Part 2, issue November 10 1999, Volume 52