The investigation of the non-linearity of the Leavitt law is a topic that began more than seven decades ago, when some of the studies in this field found that the Leavitt law has a break at about ten days.The goal of this work is to investigate a possible statistical cause of this nonlinearity. By applying linear regressions to OGLE-II and OGLE-IV data, we find that, in order to obtain the Leavitt law by using linear regression, robust techniques to deal with influential points and/or outliers are needed instead of the ordinary least-squares regression traditionally used. In particular, by using M-and MM-regressions we establish firmly and without doubts the linearity of the Leavitt law in the Large Magellanic Cloud, without rejecting or excluding Cepheid data from the analysis. This implies that light curves of Cepheids suggesting blending, bumps, eclipses or period changes, do not affect the Leavitt law for this galaxy. For the SMC, including this kind of Cepheids, it is not possible to find an adequate model, probably due to the geometry of the galaxy. In that case, a possible influence of these stars could exist.
The process of fused deposition material (FDM) was used to manufacture propellant grains of Acrylonitrile Butadiene Styrene (ABS) as novel rocket fuel grain, with three types of geometry in the burning port. These solid fuel grains were used to measure the typical characteristics of combustion in rocket motors such as thrust and pressure inside the combustion chamber, seeking to obtain preliminary characteristics of operation and analyze the effect of combustion port geometry on pressure and thrust, using Multivariate Analysis of Variance (MANOVA) as statistical method. Two of the three geometries were manufactured with a helical-finocyl configuration, specially designed to be fabricated by Direct Digital Manufacturing (DDM), the other one was a straight-bore geometry also by DDM. This characterization experiment was performed on a static hybrid rocket engine, designed to inject 99.98% pure nitrous oxide into a combustion chamber with capacity to withstand 6.9 MPa of pressure, with an easy-to-exchange nozzle, avoiding erosive behavior in the throat. Statistical analyses made with the ABS fuel grains, suggest a significant effect on rocket motor pressure and thrust, due to helical geometric changes made to the combustion port of solid fuel grains made by FDM manufacture process.
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