Raúl Gormaz

Collisions of rigid bodies, deformable bodies and fluids

Publisher Summary The system made of two solids is deformable because the relative position of the solids may change. This fact can be applied to a complex problem of mechanics—the collision theory. The major findings are constitutive laws, which are coherent from the thermodynamics point of view. They give robust and productive models and numerical methods, for instance—for rock avalanches and collisions of solids and fluids.

Collisions Involving Solids and Fluids

Predictive theories of instantaneous collisions involving rigid and deformable solids as well as fluids are described. They are based on the description of interior percussions to the system made of the colliding bodies. The system made of all the elements (solids or fluids) that are colliding is a deformable system: its form changes even if it is made of rigid elements! If the duration of a collision is small compared to the duration of the evolution, we assume that the collision is instantaneous; thus the velocities are discontinuous We describe the collision of a point with a fixed plane and the simultaneous collisions of a collection of rigid bodies. The impact of an hammer with a bar is an example of collisions of deformables bodies. Experiments show the adequation of the theory. The collision of fluids and solids is illustrated by the description of the belly flop of a diver in a swimming pool.

ICT Supported Learning Rises Math Achievement in Low Socio Economic Status Schools

Sustained improvement in student achievement on national standardized tests for low socio economic status (SES) districts is critical for reducing gaps in educational inequality. We report the results of 3 years of implementation of an ICT web-based learning environment in all 11 public schools of a low SES urban district in Chile. This includes 43 fourth grade classes and 1,355 students. This is a Computer Aided Instruction program that promotes whole class collaborative learning with peer support. Effect size on the national standardized fourth grade math test is 0.33, which is three times the national improvement level over the same period and five times the improvement made by a neighboring district with a similar population. On the other hand, the same students did not make any improvements on the national standardized language test. Since each class was taught by the same teacher, only without ICT, we can therefore discount the teacher effect.

A class of multivariate de Boor–Fix formulae

A family of Marsden identities and de Boor-Fix formulae in the multivariate case are proposed. A general framework to define dual bases is presented, which requires neither polynomial functions, nor univariate functions. Nevertheless, the main focus is the multivariate polynomial case. The relation between polar form and dual bases is presented in this multivariate polynomial case.

Mathematical study of transport phenomena along a tuyere of the Teniente converter

This paper presents a comprehensive mathematical model of transport phenomena which occur along a tuyere of the Teniente converter during injection of oxygen-enriched air. Inlet pressure, gas velocity and temperature, the dimensions of the tuyere, and the properties of gas are the basic data. From these inputs, temperature distribution of the refractory walls of the converter around the tuyere as well as the velocity, pressure, and the Mach number along the pipe can be calculated. In this model, the heat transfer through the metal jacket of the tuyere and the refractory lining are duly taken into account. More precisely, a mathematical model is developed where the equations of momentum and energy of the gas are coupled with the equations of heat transfer inside the solid part. This new model couples a partial differential equation in the solid part with four ordinary differential equations in the gas flow.