A critical view on biaxial and short-beam uniaxial flexural strength tests applied to resin composites using Weibull, fractographic and finite element analyses

Objective. To evaluate the biaxial and short-beam uniaxial strength tests applied to resin composites based upon their Weibull parameters, fractographic features and stress distribution. Methods. Disk- (15 mm x 1 mm) and beam-shaped specimens (10 mm x 2 mm x 1 mm) of three commercial composites (Concept/Vigodent, CA; Heliomolar/Ivoclar-Vivadent, HE; Z250/3M ESPE, FZ) were prepared. After 48h dry storage at 37 degrees C, disks and beams were submitted to piston-on-three-balls (BI) and three-point bending (UNI) tests, respectively. Data were analyzed by Weibull statistics. Fractured surfaces were observed under stereomicroscope and scanning electron microscope. Maximum principal stress (sigma(1)) distribution was determined by finite element analysis (FEA). Maximum sigma(1-BI) and sigma(1-UNI) were compared to FZ strengths calculated by applying the average failure loads to the analytical equations (sigma(a-BI) and sigma(a-UNI)). Results. For BI, characteristic strengths were: 169.9a (FZ), 122.4b (CA) and 104.8c (HE), and for UNI were: 160.3a (FZ), 98.2b (CA) and 91.6b (HE). Weibull moduli ( m) were similar within the same test. CA and HE presented statistically higher m for BI. Surface pores ( BI) and edge flaws ( UNI) were the most frequent fracture origins. sigma(1-BI) was 14% lower than sigma(a-BI.) sigma(1-UNI) was 43% higher than sigma(a-UNI). Significance. Compared to the short-beam uniaxial test, the biaxial test detected more differences among composites and displayed less data scattering for two of the tested materials. Also, biaxial strength was closer to the material`s strength estimated by FEA. (C) 2009 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Models involving two inverse Weibull distributions

In this paper, we look at three models (mixture, competing risk and multiplicative) involving two inverse Weibull distributions. We study the shapes of the density and failure-rate functions and discuss graphical methods to determine if a given data set can be modelled by one of these models. (C) 2001 Elsevier Science Ltd. All rights reserved.

n-fold Weibull multiplicative model

In this paper we study the n-fold multiplicative model involving Weibull distributions and examine some properties of the model. These include the shapes for the density and failure rate functions and the WPP plot. These allow one to decide if a given data set can be adequately modelled by the model. We also discuss the estimation of model parameters based on the WPP plot. (C) 2001 Elsevier Science Ltd. All rights reserved.

A modified Weibull distribution

A new lifetime distribution capable of modeling a bathtub-shaped hazard-rate function is proposed. The proposed model is derived as a limiting case of the Beta Integrated Model and has both the Weibull distribution and Type I extreme value distribution as special cases. The model can be considered as another useful 3-parameter generalization of the Weibull distribution. An advantage of the model is that the model parameters can be estimated easily based on a Weibull probability paper (WPP) plot that serves as a tool for model identification. Model characterization based on the WPP plot is studied. A numerical example is provided and comparison with another Weibull extension, the exponentiated Weibull, is also discussed. The proposed model compares well with other competing models to fit data that exhibits a bathtub-shaped hazard-rate function.

Study of n-fold Weibull competing risk model

This paper deals with an n-fold Weibull competing risk model. A characterisation of the WPP plot is given along with estimation of model parameters when modelling a given data set. These are illustrated through two examples. A study of the different possible shapes for the density and failure rate functions is also presented. (C) 2003 Elsevier Ltd. All rights reserved.

An Extension of Gompertzian Growth Dynamics Weibull and Frechet Models

In this work a new probabilistic and dynamical approach to an extension of the Gompertz law is proposed. A generalized family of probability density functions, designated by Beta* (p, q), which is proportional to the right hand side of the Tsoularis-Wallace model, is studied. In particular, for p = 2, the investigation is extended to the extreme value models of Weibull and Frechet type. These models, described by differential equations, are proportional to the hyper-Gompertz growth model. It is proved that the Beta* (2, q) densities are a power of betas mixture, and that its dynamics are determined by a non-linear coupling of probabilities. The dynamical analysis is performed using techniques of symbolic dynamics and the system complexity is measured using topological entropy. Generally, the natural history of a malignant tumour is reflected through bifurcation diagrams, in which are identified regions of regression, stability, bifurcation, chaos and terminus.

Symbolic dynamics and big bang bifurcation in Weibull-Gompertz-Fréchet's growth models

In this paper, motivated by the interest and relevance of the study of tumor growth models, a central point of our investigation is the study of the chaotic dynamics and the bifurcation structure of Weibull-Gompertz-Fréchet's functions: a class of continuousdefined one-dimensional maps. Using symbolic dynamics techniques and iteration theory, we established that depending on the properties of this class of functions in a neighborhood of a bifurcation point PBB, in a two-dimensional parameter space, there exists an order regarding how the infinite number of periodic orbits are born: the Sharkovsky ordering. Consequently, the corresponding symbolic sequences follow the usual unimodal kneading sequences in the topological ordered tree. We verified that under some sufficient conditions, Weibull-Gompertz-Fréchet's functions have a particular bifurcation structure: a big bang bifurcation point PBB. This fractal bifurcations structure is of the so-called "box-within-a-box" type, associated to a boxe ω1, where an infinite number of bifurcation curves issues from. This analysis is done making use of fold and flip bifurcation curves and symbolic dynamics techniques. The present paper is an original contribution in the framework of the big bang bifurcation analysis for continuous maps.

Kaasun jakauma paineellisissa sulpunkäsittelylaitteissa

Työn tarkoituksena oli tutkia kuinka kaasukuplat jakautuvat sellususpensioon, kun prosessiolosuhteita muutetaan. Kuplien kokojakauman avulla pyritään kartoittamaan kuinka kaasukuplat pilkkoutuvat ja onko olemassa raja-arvoa, milloin tehon lisäys ei enää pilko sellususpensiossa olevia kuplia pienemmiksi. Jakaumien avulla voidaan mahdollisesti kehittää kaasunpoistoa. Työssä selvitettiin voidaanko kameratekniikkaa käyttää kuplakokojen määrittämiseen sellusulpusta. Läpinäkymätön sellumassa tarjoaa kuvaukselle haasteellisen ympäristön. Myöskään kirjallisuudessa ei vastaavaa menetelmää aikaisemmin oltu käytetty. Kuvatusta materiaalista laskettiin kuplien halkaisijat, joita pyrittiin tarkastelemaan tilastollisesti. Tilastollinen tarkastelu toi eroja mittauspisteiden välille. Kuplien halkaisijoiden perusteella mallinnettiin kuplakokoon vaikuttavat prosessisuureet lineaarisella regressioanalyysillä. Mallinnuksen perusteella saatiinvasteisiin vaikuttavat riippumattomat muuttujat ja niiden matemaattiset malliyhtälöt. Tuloksina saatiin selville, että kuplien kokojakaumissa on eroja sekoitussäiliön eri puolilla. Sekoitussäiliössä suurten kuplien suhteellinen osuus kasvaa kaasupitoisuuden ja sakeuden noustessa. Mallinnuksen tärkeimpänä tuloksena voidaan todeta, että sakeus ja kaasutilavuus vaikuttavat kuplakokoon kasvattavasti. Kierrosnopeuden kasvattaminen pienentää kuplakokoa. Visuaalisen informaation avulla on helpompi ymmärtää kuinka kuplat käyttäytyvät.

Apteeraustuloksen mittarina käytetyn jakauma-asteen tilastollisista ominaisuuksista

Seloste artikkelista: Koskela, L., Sinha, B. K. & Nummi, T. 2007. Some aspects of the sampling distribution of the apportionment index and related inference. Silva Fennica 41 (4) : 699-715

Foam-forming properties of Ilex paraguariensis (mate) saponin: foamability and foam lifetime analysis by Weibull equation

Saponins are natural soaplike foam-forming compounds widely used in foods, cosmetic and pharmaceutical preparations. In this work foamability and foam lifetime of foams obtained from Ilex paraguariensis unripe fruits were analyzed. Polysorbate 80 and sodium dodecyl sulfate were used as reference surfactants. Aiming a better data understanding a linearized 4-parameters Weibull function was proposed. The mate hydroethanolic extract (ME) and a mate saponin enriched fraction (MSF) afforded foamability and foam lifetime comparable to the synthetic surfactants. The linearization of the Weibull equation allowed the statistical comparison of foam decay curves, improving former mathematical approaches.

Uso da função Weibull de três parâmetros em um modelo de distribuição diamétrica para plantios de eucalipto submetidos a desbaste

O objetivo deste estudo foi propor um modelo de distribuição diamétrica para povoamentos de eucalipto submetidos ao desbaste, com a inclusão do parâmetro de locação da função Weibull. Essa função foi ajustada a dados de 48 parcelas permanentes instaladas em um povoamento desbastado de um clone híbrido de eucalipto (Eucalyptus grandis x Eucalyptus urophylla), localizado na região Nordeste do Estado da Bahia, Brasil. A aderência foi avaliada pelo teste de Kolmogorov-Smirnorv (K-S). A redistribuição teórica dos diâmetros foi feita a partir de equações lineares e não lineares entre os parâmetros da função Weibull em uma idade futura e os parâmetros, em uma idade atual e associados a algumas características do povoamento em idades atual e futura. O sistema de equações gerado foi avaliado utilizando-se o coeficiente de determinação ajustado e o coeficiente de correlação entre frequências observadas e frequências estimadas e a análise gráfica dos resíduos. O sistema proposto resultou em estimativas precisas e consistentes de crescimento por classe de diâmetro.

Avaliação do ajuste das funções weibull e hiperbólica a dados de povoamentos de eucalipto submetidos a desbaste

O objetivo deste estudo foi avaliar as funções de Weibull e Hiperbólica quanto à capacidade de descrição da estrutura diamétrica de povoamentos de eucalipto submetidos a desbaste. As funções com quatro e três parâmetros foram ajustadas a dados de 48 parcelas permanentes instaladas em um povoamento desbastado de um clone híbrido de eucalipto (Eucalyptus grandis x Eucalyptus urophylla), localizado na região Nordeste do Estado da Bahia. Essas parcelas foram mensuradas em 10 ocasiões, a partir de 27 meses de idade. Foi avaliado, também, o ajuste da função Weibull de dois parâmetros por aproximação linear. A aderência foi avaliada pelo teste de Kolmogorov-Smirnov. Também, foram comparadas as somas de quadrados dos resíduos (SQR), dos diferentes ajustamentos. Todas as funções apresentaram aderência aos dados (P>0,01). A função hiperbólica apresentou menor soma de quadrados de resíduos e menores valores para o teste de aderência. A função Weibull, quando ajustada por aproximação linear, apresentou os maiores valores de soma de quadrado de resíduos e de significância no teste de aderência. Foi comprovada a ineficiência do ajuste da função Weibull por aproximação linear.