Star Formation Conditions in Nearby Galaxies

The understanding of gravitational stability of galactic disks against star formation, the interplay of atomic and molecular components of the interstellar medium in a galaxy and its physical conditions, namely temperature and density, are important to gain a deeper insight into star formation. Nearby galaxies like the spiral galaxy M51 or the southern starburst galaxies NGC4945 and Circinus offer excellent opportunities to investigate these topics over a complete galactic disk or parts of the galaxy. A suitable tracer to study the molecular part of the gaseous component of galaxies is the CO molecule. It is the second most abundant molecule after H2 in the interstellar medium, its lower lying transition are excited at typical conditions of molecular clouds and the rotational transitions lie in the radio window. Thus, CO emission can penetrate throughout galactic disks and is observable from the ground. Apart from complementary data from the literature, we use observations of 12CO 2—1, 12CO 4--3, and 13CO 2--1 in this thesis. Additionally, the [CI] 3P1-3P0 fine structure line was observed to study the physical conditions in the central regions of galaxies. In the first part of this thesis, the nearby spiral galaxy M51 is used as a sample source to investigate the onset of star formation. CO, HI, radio-continuum, dust, and stellar maps of M51 are combined to study star formation rate, the H2/HI transition, the gas-to-dust ratios, the stability of the disk against gravitational collapse, and properties of the giant molecular clouds. Parts of the results have been published in Astronomy and Astrophysics (461,143) in 2007 and are submitted to Astronomy and Astrophysics, 2008 for publication. We use the first complete 12CO 2--1 map of M51 including the companion galaxy NGC5195 observed with HERA at the IRAM-30m telescope to trace the molecular gas. Complementary \HI\ VLA data is used to study the atomic gas distribution and the combined total gas surface density. The total gas density is compared to the dust density from 850 microm SCUBA data. Using radio continuum VLA data, we compute the Schmidt law in M51, an empirical relation of total gas density and star formation rate. The velocity dispersions of the molecular and atomic gas, indicating the local resistance against gravitational collapse, are computed. For the Toomre Q parameter of the disk, a measure of the gravitational stability, we combine the stellar surface density derived from the 2MASS K-band survey with total gas surface density and velocity dispersions of stellar, atomic ,and molecular components of the disk. The Gaussclumps-algorithm is applied to decompose the 12CO 2--1 emission into molecular cloud complexes with masses down to the resolution limit. Subsequently, we study the clump mass spectrum of the identified molecular clouds. The ratio of molecular to atomic gas surface density shows a close-to powerlaw dependence on the hydrostatic pressure Phydro. The distribution of the gas surface density, Sigma-gas, in M51 shows an underlying exponential distribution with a scale-length of h-gas=7.6kpc representing 55% of the total gas mass, comparable to the properties of the exponential dust disk. The total gas surface density and the star formation rate per unit area and time Sigma-SFR are correlated. This empirical relation is also found in other galaxies and is the so called local Schmidt law. We fitted a local Schmidt law with a power-law index of n=1.4 +-0.6 to our data in M51. In contrast to the velocity widths observed in HI , the CO velocity dispersion shows enhanced line widths in the spiral arms compared to the interarm regions. The threshold of gravitational stability according to the total Toomre parameter, Q-tot=1, is close to the results in the radial averages: Q-tot varies from 1.5-3. A map of Q-tot shows values around 1 on the spiral arms indicating self-regulation. The clump mass spectrum extends over a mass range of 4.9 10e(5) M-sun to 1.2 10e(8) M-sun and shows a powerlaw index alpha= 1.71 +-0.24. The positions of the 16 most massive identified clumps in the inner part follow the shape of a logarithmic spiral. The second part of this thesis deals with the estimation of the physical conditions in the central regions of the star burst galaxies NGC4945 and Circinus from molecular line observations. The temperature, molecular density, and column densities of CO and atomic carbon are predicted. We published parts of this analysis in Astronomy and Astrophysics (479,75) in 2008. The new NANTEN2 4m sub-millimeter telescope in Pampa La Bola, Chile, enabled us to observe for the first time CO 4--3 and [CI] 3P1-3P0 in the centers of both galaxies at linear scales of 682 pc and 732 pc, respectively. We compute the cooling curves of 12CO and 13CO using radiative transfer modeling and estimate the temperature, density, and column density of CO and [CI]. The centers of NGC 4945 and Circinus exhibit CI 3P1-3P0 luminosities of 91 and 67Kkm/s kpc2, respectively. The CI 3P1-3P0/CO 4--3 ratio of integrated intensities are large at 1.2 in NGC 4945 and 2.8 in Circinus. Combining previous CO J= 1--0 , 2--1 and 3--2 and 13CO J= 1-0 , 2-1 studies with our new observations, the radiative transfer calculations give a range of densities, n(H2)=10e(3)-3 e(4) cm ^-3, and a wide range of kinetic temperatures, Tkin= 20-100 K, depending on the density. The estimated total [CI] cooling intensity is stronger by factors of 1-3 compared to the total CO cooling intensity. The CO/C abundance ratios are 0.2-2, similar to values found in Galactic translucent clouds. Future high-J CO and [CI] 2--1 observations will be able to better constrain the ambiguities of density and temperature

Multi-core computation of transfer matrices for strip lattices in the Potts model

The transfer-matrix technique is a convenient way for studying strip lattices in the Potts model since the compu- tational costs depend just on the periodic part of the lattice and not on the whole. However, even when the cost is reduced, the transfer-matrix technique is still an NP-hard problem since the time T(|V|, |E|) needed to compute the matrix grows ex- ponentially as a function of the graph width. In this work, we present a parallel transfer-matrix implementation that scales performance under multi-core architectures. The construction of the matrix is based on several repetitions of the deletion- contraction technique, allowing parallelism suitable to multi-core machines. Our experimental results show that the multi-core implementation achieves speedups of 3.7X with p = 4 processors and 5.7X with p = 8. The efficiency of the implementation lies between 60% and 95%, achieving the best balance of speedup and efficiency at p = 4 processors for actual multi-core architectures. The algorithm also takes advantage of the lattice symmetry, making the transfer matrix computation to run up to 2X faster than its non-symmetric counterpart and use up to a quarter of the original space

The scattering of phonons by infinitely long quantum dislocations segments and the generation of thermal transport anisotropy in a solid threaded by many parallel dislocations

A canonical quantization procedure is applied to the interaction of elastic waves --phonons-- with infinitely long dislocations that can oscillate about an equilibrium, straight line, configuration. The interaction is implemented through the well-known Peach-Koehler force. For small dislocation excursions away from the equilibrium position, the quantum theory can be solved to all orders in the coupling constant. We study in detail the quantum excitations of the dislocation line, and its interactions with phonons. The consequences for the drag on a dislocation caused by the phonon wind are pointed out. We compute the cross-section for phonons incident on the dislocation lines for an arbitrary angle of incidence. The consequences for thermal transport are explored, and we compare our results, involving a dynamic dislocation, with those of Klemens and Carruthers, involving a static dislocation. In our case, the relaxation time is inversely proportional to frequency, rather than directly proportional to frequency. As a consequence, the thermal transport anisotropy generated on a material by the presence of a highly-oriented array of dislocations is considerably more sensitive to the frequency of each propagating mode, and therefore, to the temperature of the material.Comment: 21 pages, 8 figure

Veamy: an extensible object-oriented C++ library for the virtual element method

This paper summarizes the development of Veamy, an object-oriented C++ library for the virtual element method (VEM) on general polygonal meshes, whose modular design is focused on its extensibility. The linear elastostatic and Poisson problems in two dimensions have been chosen as the starting stage for the development of this library. The theory of the VEM, upon which Veamy is built, is presented using a notation and a terminology that resemble the language of the finite element method (FEM) in engineering analysis. Several examples are provided to demonstrate the usage of Veamy, and in particular, one of them features the interaction between Veamy and the polygonal mesh generator PolyMesher. A computational performance comparison between VEM and FEM is also conducted. Veamy is free and open source software

Enseñanza de transformaciones isométricas en 8° básico desde la teoría de las situaciones didácticas

A partir de la teoría de las situaciones didácticas de Guy Brousseau se propone un grupo de actividades para caracterizar la traslación, rotación y reflexión de figuras planas y reconocer sus propiedades. Las actividades consisten en que, trabajando en un grupo de dos estudiantes, uno de ellos debe dar instrucciones orales para que el otro compañero o compañera replique una figura a la cual se le ha aplicado una transformación isométrica, recurriendo a los elementos que definen cada transformación. También se presentan las principales conclusiones de la aplicación de las actividades en un 8° básico de un liceo de Santiago, con el fin de realizar sugerencias y aumentar el impacto en el aprendizaje de los estudiantes