Galaxy Formation and Evolution. II. Energy Balance, Star Formation and Feed-back

In this paper we present a critical discussion of the algorithms commonly used in N-body simulations of Galaxy Formation to deal with the energy equation governing heating and cooling, to model star formation and the star formation rate, and to account for energy feed-back from stars. First, we propose our technique for solving the energy equation in presence of heating and cooling, which includes some difference with respect to the standard semi-implicit technique. Second, we examine the current criteria for the onset of the star formation activity. We suggest a new approach, in which star formaiton is let depend on the total mass density - baryonic (gas and stars) and dark matter - of the system and on the metal-dependent cooling efficiency. Third, we check and discuss the separate effects of energy (and mass) feed-back from several sources - namely supernovae, stellar winds from massive stars, and UV flux from the same objects. All the simulations are performed in the framework of the formation and evolution of a disk galaxy. We show that the inclusion of these physical phenomena has a signigicant impact on the evolution of the galaxy model.Comment: 11 pages, 6 figures, to be pubblished in MNRA

Nuevo complemento para simulaciones de ingeniería en hojas de cálculo usando métodos de continuidad homotópica

RESUMEN: Resolver modelos matemáticos representados por ecuaciones no lineales es común en la ingeniería y puede ser una tarea difícil. Los métodos de Continuidad Homotópica han mostrado ser globalmente convergentes y capaces de encontrar todas las posibles raíces de sistemas algebraicos. Con base en este tipo de métodos, se presenta un nuevo complemento para Microsoft Office Excel, SphereSolver, desarrollado con el objetivo de mejorar la capacidad de este software común, como una plataforma de computación de simulación para problemas de ingeniería. SphereSolver se aplico sobre diferentes tipos de modelos de ingeniería y en todos los casos, las ecuaciones no lineales se resolvieron con éxito. La solución con SphereSolver a los problemas seleccionados se comparo con otras técnicas de solución, por ejemplo, el método clásico de Newton, Homotópica de punto fijo y Homotopía Afín. Se observo que usando SphereSolver el intervalo de convergencia se extiende masivamente y / o se pueden encontrar raíces adicionales, es decir, se mejoro la solución. Se concluye que SphereSolver es una herramienta eficiente que se puede utilizar en Microsoft Excel para resolver problemas de ingeniería donde otros programas o herramientas tradicionales pueden fallar o presentar limitaciones.ABSTRACT: Solving models represented by non-linear equations is a common situation in engineering and can be a challenging task. Homotopy Continuation Methods have shown globally convergent behavior, capable of finding all the possible roots of algebraic systems. Based on these methods, a new Microsoft Office Excel add-in was developed, SphereSolver, aiming to enhance the ability to use this easily obtainable software as a simulation computing platform for engineering problems. SphereSolver was applied over different types of engineering models and the non-linear equations were solved successfully each time. Selected problems were solved with SphereSolver and compared with other solution tecniques, e.g., classical Newton’s method, Fixed Point homotopy or Affine Homotopy. It was observed that using SphereSolver the solution for selected problems was improved, i.e., the interval of convergence is extended massively and/or additional roots can be found. It can be concluded that SphereSolver is a new and efficient tool that can be used within Microsoft Excel for solving engineering problems where other software or traditional tools could fail or present limitations

Magnetometer calibration using inertial sensors

In this work we present a practical algorithm for calibrating a magnetometer for the presence of magnetic disturbances and for magnetometer sensor errors. To allow for combining the magnetometer measurements with inertial measurements for orientation estimation, the algorithm also corrects for misalignment between the magnetometer and the inertial sensor axes. The calibration algorithm is formulated as the solution to a maximum likelihood problem and the computations are performed offline. The algorithm is shown to give good results using data from two different commercially available sensor units. Using the calibrated magnetometer measurements in combination with the inertial sensors to determine the sensor's orientation is shown to lead to significantly improved heading estimates.Comment: 19 pages, 8 figure

Computation of the inviscid supersonic flow about cones at large angles of attack by a floating discontinuity approach

The technique of floating shock fitting is adapted to the computation of the inviscid flowfield about circular cones in a supersonic free stream at angles of attack that exceed the cone half-angle. The resulting equations are applicable over the complete range of free-stream Mach numbers, angles of attack and cone half-angles for which the bow shock is attached. A finite difference algorithm is used to obtain the solution by an unsteady relaxation approach. The bow shock, embedded cross-flow shock, and vortical singularity in the leeward symmetry plane are treated as floating discontinuities in a fixed computational mesh. Where possible, the flowfield is partitioned into windward, shoulder, and leeward regions with each region computed separately to achieve maximum computational efficiency. An alternative shock fitting technique which treats the bow shock as a computational boundary is developed and compared with the floating-fitting approach. Several surface boundary condition schemes are also analyzed