Planning accelerated life tests under Exponentiated-Weibull-Arrhenius model

Purpose - The purpose of this paper is to present designs for an accelerated life test (ALT). Design/methodology/approach - Bayesian methods and simulation Monte Carlo Markov Chain (MCMC) methods were used. Findings - In the paper a Bayesian method based on MCMC for ALT under EW distribution (for life time) and Arrhenius models (relating the stress variable and parameters) was proposed. The paper can conclude that it is a reasonable alternative to the classical statistical methods since the implementation of the proposed method is simple, not requiring advanced computational understanding and inferences on the parameters can be made easily. By the predictive density of a future observation, a procedure was developed to plan ALT and also to verify if the conformance fraction of the manufactured process reaches some desired level of quality. This procedure is useful for statistical process control in many industrial applications. Research limitations/implications - The results may be applied in a semiconductor manufacturer. Originality/value - The Exponentiated-Weibull-Arrhenius model has never before been used to plan an ALT. © Emerald Group Publishing Limited.

Eficiência econômica e energética de sistemas de produção de mamona nos estados de Minas Gerais e Paraná

Pós-graduação em Agronomia (Energia na Agricultura) - FCA

Eficiência energética de sistemas de produção de mamona no Estado de Minas Gerais

The objective of this study is to determine the economical and energetic efficiency of the castor bean culture in "Zona da Mata" and South of Minas Gerais. Through the method of simulation "Monte Carlo", we verified the probabilities of occurrence of the economical, cultural and energetic efficiency indexes. In relation to the production systems of castor bean in Minas Gerais in the season 2005/2006, we established that the variables price and productivity were the most noticeable for the producers from "Zona da Mata", while in the South of Minas it was productivity. We verified that the probability of the economical efficiency index to be lower than one was 43,26% for the producers from "Zona da Mata" and 39,57% for the ones from the South of Minas. The medium price received covered the medium costs of production. However, we observed that the medium costs in these regions of Minas Gerais, were over the minimum price. Regarding the energetic analysis, the results showed that the systems in the regions studied in Minas Gerasi, presented average of cultural efficiency indexes of 8,26 and 18,89. We concluded that despite the result being favorable from the energetic point of view, from the economical sustainability point of view there is the need of a more effective support policy for the castor bean, taking into consideration that the expectations of the producers with PNPB were not confirmed.

Modeling the heterogeneous ice and gas coma of Comet 103P/Hartley 2

The spectacular images of Comet 103P/Hartley 2 recorded by the Medium Resolution Instrument (MRI) and High Resolution Instrument (HRI) on board of the Extrasolar Planet Observation and Deep Impact Extended Investigation (EPOXI) spacecraft, as the Deep Impact extended mission, revealed that its bi-lobed very active nucleus outgasses volatiles heterogeneously. Indeed, CO2 is the primary driver of activity by dragging out chunks of pure ice out of the nucleus from the sub-solar lobe that appear to be the main source of water in Hartley 2's coma by sublimating slowly as they go away from the nucleus. However, water vapor is released by direct sublimation of the nucleus at the waist without any significant amount of either CO2 or icy grains. The coma structure for a comet with such areas of diverse chemistry differs from the usual models where gases are produced in a homogeneous way from the surface. We use the fully kinetic Direct Simulation Monte Carlo model of Tenishev et al. (Tenishev, V.M., Combi, M.R., Davidsson, B. [2008]. Astrophys. J. 685, 659-677; Tenishev, V.M., Combi, M.R., Rubin, M. [2011]. Astrophys. J. 732, 104-120) applied to Comet 103P/Hartley 2 including sublimating icy grains to reproduce the observations made by EPOXI and ground-based measurements. A realistic bi-lobed nucleus with a succession of active areas with different chemistry was included in the model enabling us to study in details the coma of Hartley 2. The different gas production rates from each area were found by fitting the spectra computed using a line-by-line non-LTE radiative transfer model to the HRI observations. The presence of icy grains with long lifetimes, which are pushed anti-sunward by radiation pressure, explains the observed OH asymmetry with enhancement on the night side of the coma.

The spatial distribution of water in the inner coma of Comet 9P/Tempel 1: Comparison between models and observations

The near nucleus coma of Comet 9P/Tempel 1 has been simulated with the 3D Direct Simulation Monte Carlo (DSMC) code PDSC++ (Su, C.-C. [2013]. Parallel Direct Simulation Monte Carlo (DSMC) Methods for Modeling Rarefied Gas Dynamics. PhD Thesis, National Chiao Tung University, Taiwan) and the derived column densities have been compared to observations of the water vapour distribution found by using infrared imaging spectrometer on the Deep Impact spacecraft (Feaga, L.M., A’Hearn, M.F., Sunshine, J.M., Groussin, O., Farnham, T.L. [2007]. Icarus 191(2), 134–145. http://dx.doi.org/10.1016/j.icarus.2007.04.038). Modelled total production rates are also compared to various observations made at the time of the Deep Impact encounter. Three different models were tested. For all models, the shape model constructed from the Deep Impact observations by Thomas et al. (Thomas, P.C., Veverka, J., Belton, M.J.S., Hidy, A., A’Hearn, M.F., Farnham, T.L., et al. [2007]. Icarus, 187(1), 4–15. http://dx.doi.org/10.1016/j.icarus.2006.12.013) was used. Outgassing depending only on the cosine of the solar insolation angle on each shape model facet is shown to provide an unsatisfactory model. Models constructed on the basis of active areas suggested by Kossacki and Szutowicz (Kossacki, K., Szutowicz, S. [2008]. Icarus, 195(2), 705–724. http://dx.doi.org/10.1016/j.icarus.2007.12.014) are shown to be superior. The Kossacki and Szutowicz model, however, also shows deficits which we have sought to improve upon. For the best model we investigate the properties of the outflow.

Relating in situ gas measurements to the surface outgassing properties of cometary nuclei

The sensitivity of the gas flow field to changes in different initial conditions has been studied for the case of a highly simplified cometary nucleus model. The nucleus model simulated a homogeneously outgassing sphere with a more active ring around an axis of symmetry. The varied initial conditions were the number density of the homogeneous region, the surface temperature, and the composition of the flow (varying amounts of H2O and CO2) from the active ring. The sensitivity analysis was performed using the Polynomial Chaos Expansion (PCE) method. Direct Simulation Monte Carlo (DSMC) was used for the flow, thereby allowing strong deviations from local thermal equilibrium. The PCE approach can be used to produce a sensitivity analysis with only four runs per modified input parameter and allows one to study and quantify non-linear responses of measurable parameters to linear changes in the input over a wide range. Hence the PCE allows one to obtain a functional relationship between the flow field properties at every point in the inner coma and the input conditions. It is for example shown that the velocity and the temperature of the background gas are not simply linear functions of the initial number density at the source. As probably expected, the main influence on the resulting flow field parameter is the corresponding initial parameter (i.e. the initial number density determines the background number density, the temperature of the surface determines the flow field temperature, etc.). However, the velocity of the flow field is also influenced by the surface temperature while the number density is not sensitive to the surface temperature at all in our model set-up. Another example is the change in the composition of the flow over the active area. Such changes can be seen in the velocity but again not in the number density. Although this study uses only a simple test case, we suggest that the approach, when applied to a real case in 3D, should assist in identifying the sensitivity of gas parameters measured in situ by, for example, the Rosetta spacecraft to the surface boundary conditions and vice versa.

Understanding measured water rotational temperatures and column densities in the very innermost coma of Comet 73P/Schwassmann–Wachmann 3 B

Direct sublimation of a comet nucleus surface is usually considered to be the main source of gas in the coma of a comet. However, evidence from a number of comets including the recent spectacular images of Comet 103P/Hartley 2 by the EPOXI mission indicates that the nucleus alone may not be responsible for all, or possibly at times even most, of the total amount of gas seen in the coma. Indeed, the sublimation of icy grains, which have been injected into the coma, appears to constitute an important source. We use the fully-kinetic Direct Simulation Monte Carlo model of Tenishev et al. (Tenishev, V.M., Combi, M.R., Davidsson, B. [2008]. Astrophys. J., 685, 659−677; Tenishev, V.M., Combi, M.R., Rubin, M. [2011]. Astrophys. J., 732) to reproduce the measurements of column density and rotational temperature of water in Comet 73P-B/Schwassmann–Wachmann 3 obtained with a very high spatial resolution of ∼30 km using IRCS/Subaru in May 2006 (Bonev, B.P., Mumma, M.J., Kawakita, H., Kobayashi, H., Villanueva, G.L. [2008]. Icarus, 196, 241−248). For gas released solely from the cometary nucleus at a heliocentric distance of 1 AU, modeled rotational temperatures start at 110 K close to the surface and decrease to only several tens of degrees by 10–20 nucleus radii. However, the measured decay of both rotational temperature and column density with distance from the nucleus is much slower than predicted by this simple model. The addition of a substantial (distributed) source of gas from icy grains in the model slows the decay in rotational temperature and provides a more gradual drop in column density profiles. Together with a contribution of rotational heating of water molecules by electrons, the combined effects allow a much better match to the IRCS/Subaru observations. From the spatial distributions of water abundance and temperature measured in 73P/SW3-B, we have identified and quantified multiple mechanisms of release. The application of this tool to other comets may permit such studies over a range of heliocentric and geocentric distances.

The calculation of Afρ and mass loss rate for comets

Ab initio calculations of Afρ are presented using Mie scattering theory and a Direct Simulation Monte Carlo (DSMC) dust outflow model in support of the Rosetta mission and its target 67P/Churyumov-Gerasimenko (CG). These calculations are performed for particle sizes ranging from 0.010 μm to 1.0 cm. The present status of our knowledge of various differential particle size distributions is reviewed and a variety of particle size distributions is used to explore their effect on Afρ , and the dust mass production View the MathML sourcem˙. A new simple two parameter particle size distribution that curtails the effect of particles below 1 μm is developed. The contributions of all particle sizes are summed to get a resulting overall Afρ. The resultant Afρ could not easily be predicted a priori and turned out to be considerably more constraining regarding the mass loss rate than expected. It is found that a proper calculation of Afρ combined with a good Afρ measurement can constrain the dust/gas ratio in the coma of comets as well as other methods presently available. Phase curves of Afρ versus scattering angle are calculated and produce good agreement with observational data. The major conclusions of our calculations are: – The original definition of A in Afρ is problematical and Afρ should be: qsca(n,λ)×p(g)×f×ρqsca(n,λ)×p(g)×f×ρ. Nevertheless, we keep the present nomenclature of Afρ as a measured quantity for an ensemble of coma particles.– The ratio between Afρ and the dust mass loss rate View the MathML sourcem˙ is dominated by the particle size distribution. – For most particle size distributions presently in use, small particles in the range from 0.10 to 1.0 μm contribute a large fraction to Afρ. – Simplifying the calculation of Afρ by considering only large particles and approximating qsca does not represent a realistic model. Mie scattering theory or if necessary, more complex scattering calculations must be used. – For the commonly used particle size distribution, dn/da ∼ a−3.5 to a−4, there is a natural cut off in Afρ contribution for both small and large particles. – The scattering phase function must be taken into account for each particle size; otherwise the contribution of large particles can be over-estimated by a factor of 10. – Using an imaginary index of refraction of i = 0.10 does not produce sufficient backscattering to match observational data. – A mixture of dark particles with i ⩾ 0.10 and brighter silicate particles with i ⩽ 0.04 matches the observed phase curves quite well. – Using current observational constraints, we find the dust/gas mass-production ratio of CG at 1.3 AU is confined to a range of 0.03–0.5 with a reasonably likely value around 0.1.

Comparison of 3D kinetic and hydrodynamic models to ROSINA-COPS measurements of the neutral coma of 67P/Churyumov-Gerasimenko

67P/Churyumov-Gerasimenko (67P) is a Jupiter-family comet and the object of investigation of the European Space Agency mission Rosetta. This report presents the first full 3D simulation results of 67P’s neutral gas coma. In this study we include results from a direct simulation Monte Carlo method, a hydrodynamic code, and a purely geometric calculation which computes the total illuminated surface area on the nucleus. All models include the triangulated 3D shape model of 67P as well as realistic illumination and shadowing conditions. The basic concept is the assumption that these illumination conditions on the nucleus are the main driver for the gas activity of the comet. As a consequence, the total production rate of 67P varies as a function of solar insolation. The best agreement between the model and the data is achieved when gas fluxes on the night side are in the range of 7% to 10% of the maximum flux, accounting for contributions from the most volatile components. To validate the output of our numerical simulations we compare the results of all three models to in situ gas number density measurements from the ROSINA COPS instrument. We are able to reproduce the overall features of these local neutral number density measurements of ROSINA COPS for the time period between early August 2014 and January 1 2015 with all three models. Some details in the measurements are not reproduced and warrant further investigation and refinement of the models. However, the overall assumption that illumination conditions on the nucleus are at least an important driver of the gas activity is validated by the models. According to our simulation results we find the total production rate of 67P to be constant between August and November 2014 with a value of about 1 × 10²⁶ molecules s⁻¹.

Transport and Distribution of Hydroxyl Radicals and Oxygen Atoms from H2O Photodissociation in the Inner Coma of Comet 67P/Churyumov-Gerasimenko

With a combination of the Direct Simulation Monte Carlo (DSMC) calculation and test particle computation, the ballistic transport process of the hydroxyl radicals and oxygen atoms produced by photodissociation of water molecules in the coma of comet 67P/Churyumov-Gerasimenko is modelled. We discuss the key elements and essential features of such simulations which results can be compared with the remote-sensing and in situ measurements of cometary gas coma from the Rosetta mission at different orbital phases of this comet.

Comparative Analysis of the Opposite Rotating Cylinders Impact over Couette Flow for Rarefied Gas

Петър Господинов, Добри Данков, Владимир Русинов, Стефан Стефанов - Иследвано е цилиндрично течение на Кует на разреден газ в случая на въртене на два коаксиални цилиндъра с еднакви по големина скорости, но в различни посоки. Целта на изследването е да се установи влиянието на малки скорости на въртене върху макрохарактеристиките – ρ, V , . Числените резултати са получени чрез използване на DSMC и числено решение на уравненията на Навие-Стокс за относително малки (дозвукови) скорости на въртене. Установено е добро съвпадение на резултатите получени по двата метода за Kn = 0.02. Установено е, че съществува “стационарна” точка за плътността и скоростта. Получените резултати са важни при решаването на неравнини, задачи от микрофлуидиката с отчитане на ефектите на кривината. Ключови думи: Механика на флуидите, Кинетична теория, Разреден газ, DSMC

Lattice Boltzmann method for flow and heat transfer in microgeometries

Recent technological developments have made it possible to design various microdevices where fluid flow and heat transfer are involved. For the proper design of such systems, the governing physics needs to be investigated. Due to the difficulty to study complex geometries in micro scales using experimental techniques, computational tools are developed to analyze and simulate flow and heat transfer in microgeometries. However, conventional numerical methods using the Navier-Stokes equations fail to predict some aspects of microflows such as nonlinear pressure distribution, increase mass flow rate, slip flow and temperature jump at the solid boundaries. This necessitates the development of new computational methods which depend on the kinetic theory that are both accurate and computationally efficient. In this study, lattice Boltzmann method (LBM) was used to investigate the flow and heat transfer in micro sized geometries. The LBM depends on the Boltzmann equation which is valid in the whole rarefaction regime that can be observed in micro flows. Results were obtained for isothermal channel flows at Knudsen numbers higher than 0.01 at different pressure ratios. LBM solutions for micro-Couette and micro-Poiseuille flow were found to be in good agreement with the analytical solutions valid in the slip flow regime (0.01 < Kn < 0.1) and direct simulation Monte Carlo solutions that are valid in the transition regime (0.1 < Kn < 10) for pressure distribution and velocity field. The isothermal LBM was further extended to simulate flows including heat transfer. The method was first validated for continuum channel flows with and without constrictions by comparing the thermal LBM results against accurate solutions obtained from analytical equations and finite element method. Finally, the capability of thermal LBM was improved by adding the effect of rarefaction and the method was used to analyze the behavior of gas flow in microchannels. The major finding of this research is that, the newly developed particle-based method described here can be used as an alternative numerical tool in order to study non-continuum effects observed in micro-electro-mechanical-systems (MEMS).

Lattice Boltzmann Method for Flow and Heat Transfer in Microgeometries

Recent technological developments have made it possible to design various microdevices where fluid flow and heat transfer are involved. For the proper design of such systems, the governing physics needs to be investigated. Due to the difficulty to study complex geometries in micro scales using experimental techniques, computational tools are developed to analyze and simulate flow and heat transfer in microgeometries. However, conventional numerical methods using the Navier-Stokes equations fail to predict some aspects of microflows such as nonlinear pressure distribution, increase mass flow rate, slip flow and temperature jump at the solid boundaries. This necessitates the development of new computational methods which depend on the kinetic theory that are both accurate and computationally efficient. In this study, lattice Boltzmann method (LBM) was used to investigate the flow and heat transfer in micro sized geometries. The LBM depends on the Boltzmann equation which is valid in the whole rarefaction regime that can be observed in micro flows. Results were obtained for isothermal channel flows at Knudsen numbers higher than 0.01 at different pressure ratios. LBM solutions for micro-Couette and micro-Poiseuille flow were found to be in good agreement with the analytical solutions valid in the slip flow regime (0.01 < Kn < 0.1) and direct simulation Monte Carlo solutions that are valid in the transition regime (0.1 < Kn < 10) for pressure distribution and velocity field. The isothermal LBM was further extended to simulate flows including heat transfer. The method was first validated for continuum channel flows with and without constrictions by comparing the thermal LBM results against accurate solutions obtained from analytical equations and finite element method. Finally, the capability of thermal LBM was improved by adding the effect of rarefaction and the method was used to analyze the behavior of gas flow in microchannels. The major finding of this research is that, the newly developed particle-based method described here can be used as an alternative numerical tool in order to study non-continuum effects observed in micro-electro-mechanical-systems (MEMS).

Modélisation incrémentale par méthode bayésienne

Les modèles incrémentaux sont des modèles statistiques qui ont été développés initialement dans le domaine du marketing. Ils sont composés de deux groupes, un groupe contrôle et un groupe traitement, tous deux comparés par rapport à une variable réponse binaire (le choix de réponses est « oui » ou « non »). Ces modèles ont pour but de détecter l’effet du traitement sur les individus à l’étude. Ces individus n’étant pas tous des clients, nous les appellerons : « prospects ». Cet effet peut être négatif, nul ou positif selon les caractéristiques des individus composants les différents groupes. Ce mémoire a pour objectif de comparer des modèles incrémentaux d’un point de vue bayésien et d’un point de vue fréquentiste. Les modèles incrémentaux utilisés en pratique sont ceux de Lo (2002) et de Lai (2004). Ils sont initialement réalisés d’un point de vue fréquentiste. Ainsi, dans ce mémoire, l’approche bayésienne est utilisée et comparée à l’approche fréquentiste. Les simulations sont e ectuées sur des données générées avec des régressions logistiques. Puis, les paramètres de ces régressions sont estimés avec des simulations Monte-Carlo dans l’approche bayésienne et comparés à ceux obtenus dans l’approche fréquentiste. L’estimation des paramètres a une influence directe sur la capacité du modèle à bien prédire l’effet du traitement sur les individus. Nous considérons l’utilisation de trois lois a priori pour l’estimation des paramètres de façon bayésienne. Elles sont choisies de manière à ce que les lois a priori soient non informatives. Les trois lois utilisées sont les suivantes : la loi bêta transformée, la loi Cauchy et la loi normale. Au cours de l’étude, nous remarquerons que les méthodes bayésiennes ont un réel impact positif sur le ciblage des individus composant les échantillons de petite taille.