Weibull Equation Research Articles

An equation of drying kinetics for cementitious materials

ABSTRACTConcrete structures are often subjected to drying in the natural environment. To simulate moisture transport in concrete during drying, a continuum model is commonly used, which generally requires the measured water vapor desorption isotherm as input data to address the equilibrium between liquid phase and water vapor at a given temperature. The main problem in measuring desorption isotherms is that the sample needs very long time to reach mass equilibrium at a certain relative humidity. To improve the method of measurement of sorption isotherms, we proposed to use Weibull equation to determine the mass loss at the infinite time. However, Weibull equation does not work well with the anomalous drying kinetics that were recently reported in the literature. In this paper, based on the theory of dual-porosity, a new equation is proposed by separating the moisture transport in the large and small pores to estimate the drying kinetics for cementitious materials. Fitting the drying kinetics measured by the dynamic vapor sorption analyzer shows that the newly developed equation has a very high capability for a large range of relative humidities, especially for the anomalous drying kinetics. This paper also demonstrates that using the proposed equation can reduce the duration of measuring desorption isotherms.

Construction and evaluation in vitro and in vivo of tedizolid phosphate loaded cationic liposomes

First, the SA-TDZA-Lips were prepared by reverse-phase evaporation method. Then, the drug release behaviour was evaluated by dynamic membrane dialysis in vitro and the preliminary safety was evaluated by haemolysis method. Finally, with tedizolid phosphate injection (TDZA-Inj) and tedizolid phosphate loaded liposomes (TDZA-Lips) as the control groups, the pharmacokinetic characteristic and tissues distribution of SA-TDZA-Lips were evaluated after intravenous injection. As a result, the stearylamine modified tedizolid phosphate liposomal delivery system was constructed successfully and the particle size was 194.9 ± 2.93 nm. The encapsulation efficiency (EE) was 53.52 ± 2.18%. The in vitro release of SA-TDZA-Lips was in accordance with Weibull equation. And there was no haemolysis happened, which indicated good preliminary safety for injection. The results of pharmacokinetics showed that the t1/2β increased by 0.74 times and 0.51 times higher than that of TDZA-Inj group and TDZA-Lips group, respectively. The MRT of SA-TDZA-Lips was 1.30 and 1.09 times higher than that of TDZA-Inj group and TDZA-Lips group, respectively. The AUC was 2.40 times and 0.23 times higher than that of TDZA-Inj group and TDZA-Lips group, respectively. The tissue distribution results showed that the relative uptake rate (Re) of TDZA in the lung was 1.527, which indicated the targeting. In conclusion, the SA-TDZA-Lips prepared in this study had several advantages like positive charge, strong cell affinity, prolonged circulation time in vivo, sustained release effect, and increased drug concentration in lungs. All advantages above provided significant clinical value of application for the treatment of bacterial pneumonia with tedizolid phosphate.

Forecasting Spring Emergence of the Asian Corn Borer, Ostrinia furnacalis (Lepidoptera: Crambidae), Based on Postdiapause Development Rate.

This study was conducted to develop temperature-dependent postdiapause development models of overwintering larvae of the Asian corn borer, Ostrinia furnacalis Guenée (Lepidoptera: Crambidae), and to evaluate the models' forecasting accuracy using spring adult emergence data. Overwintering larvae were collected at three different times: 24 February (first), 23 March (second), and 25 April (third), 2005. The developmental periods of each collection colony were measured at eight constant temperatures, and those developmental rates were modeled with linear and nonlinear regression. One linear and three nonlinear models provided good fits of developmental rate to temperature across all colonies (r2 = 0.96-0.99). The distribution of development completion time was modeled with a Weibull equation that fit data from the second (r2 = 0.92) and third (r2 = 0.97) colonies better than the first (r2 = 0.87). A Lactin 2 model based on data from the first colony was statistically the best model to describe the relationship between temperature and the postdiapause development rate of O. furnacalis (r2adj = 0.99). However, validation results based on the field data showed that the Logan 6 model combined with the Weibull model (based on the second colony) was well describing spring adult emergence patterns up to 50% cumulative emergence date.

Effect of fracture toughness on vertical split rim failure in railway wheels

Vertical split rim (VSR) cracks are the most common cause for the removal of broken or cracked heavy haul car wheels in North America. This failure mode is characterized by rapid, unstable crack propagation in the hoop or in the tangential direction. To investigate the methods to prevent VSRs, an understanding of how the service loads correlate to their occurrence is necessary. In this study, a finite element analysis is conducted to evaluate the rim stresses below the tread surface during rolling contact between the wheel tread and the rail. Then, the stress intensity factor is calculated using the stress distribution in the wheel rim obtained using the finite element analysis. The results of the analysis show that axial residual tensile stress, which contributes to unstable vertical crack propagation, increases at deeper positions below the tread surface owing to cyclic rolling contact. These results indicate that a vertical crack can propagate rapidly below the tread surface. The fracture toughness of the wheel steel is measured using Charpy impact tests. The results of the test show that Weibull distribution enables the approximation of the relationship between fracture probability and fracture toughness. To evaluate the effect of the fracture toughness of wheel steel on the differences in VSR crack probability, a comparison between high fracture toughness wheels and conventional Class-C wheels is made. The VSR rate can be predicted from the stress intensity factor and Weibull equation for fracture toughness. The prediction results show that the VSR rate of high fracture toughness wheels is only 5% of that of conventional Class-C wheels. Therefore, high fracture toughness steel wheels are considered to have a higher resistance to VSR cracks compared with conventional Class-C wheels.

Effect of Cu(II) on degradation and decolorization of rhodamine B in subcritical water

In this paper, subcritical water, an environmentally friendly solvent, was employed to degrade rhodamine B, which served as a model dye in textile industrial effluents. The effect of Cu(II) on the degradation of rhodamine B was evaluated. Further, the degradation kinetics of rhodamine B in subcritical water was evaluated via a Weibull model. The results show that subcritical water could efficiently degrade and decolorize rhodamine B. The addition of Cu(II) into subcritical water could accelerate the degradation of rhodamine B and lower the temperature for its complete degradation. The Weibull equation could well express the degradation kinetics of rhodamine B. The calculated rate constants showed Arrhenius behavior and presented high correlation coefficients. The activation energy was 109.4 kJ/mol for subcritical water degradation of rhodamine B, whereas it became lower(93.4 kJ/mol) when Cu(II) was added to the subcritical water. The frequency factors for the degradation of rhodamine B by subcritical water without and with Cu(II) were calculated to be 1.0×1011 and 3.2×109 min‒1, respectively. The above results indicate that subcritical water treatment is a promising process for degrading and decolorizing textile dyes. The results will provide a theoretic support for the industrial application of subcritical water treatment.

Modeling Variation in Crown Profile with Tree Status and Cardinal Directions for Planted Larix olgensis Henry Trees in Northeast China

Crown profile models were developed for north, east, south, and west crown directions of dominant trees, intermediate trees, and suppressed trees in planted stands of Larix olgensis Henry in Northeast China. A total of 139 sample trees were randomly selected, and all branches of each tree were measured. A segmented power equation, segmented polynomial equation, modified Weibull equation, and Kozak equation were selected as the candidate models. A traditional approach that did not consider the differences between tree status and crown directions was also developed. Three steps were conducted to analyze the effect of tree status (dominant, intermediate, and suppressed tree) and crown direction (north, east, south, and west) on the crown profiles using a dummy variable approach. Step 1 considered only tree status, Step 2 considered only crown direction, and Step 3 took both tree status and crown direction into account. Nonlinear mixed-effects model was used to express the effect of individual tree level on crown shape, and was also compared to the ordinary least-squares and generalized least-squares model. The results demonstrated that the modified Kozak equation showed good performance in the crown profile description. The nonlinear mixed-effects model significantly improved the model performance compared to the ordinary least-squares and generalized least-squares model. There were differences among the crown profiles among the four directions of dominant, intermediate, and suppressed trees. South-oriented crowns had the tendency to be the largest, which is likely to be mainly a result of light conditions. The competition status of the subject tree was the main reason leading to an asymmetric crown. Individual trees with strong competition levels had smaller crowns.

Inactivation of Listeria monocytogenes on Frozen Red Raspberries by Using UV-C Light

In this study, the efficacy of UV-C treatment was determined on the reduction of foodborne pathogens on artificially contaminated frozen food surfaces. At first, the UV-C inactivation rates on 100 μl of the respective cocktails of Escherichia coli O157:H7, Salmonella , and Listeria monocytogenes covered underneath 0.5-cm-thick ice were examined. Simultaneously, the energy percentage of UV-C transmitted through the ice was determined. The experiments showed that more than 65% of the UV-C light energy passed through the ice and that UV-C susceptibility was in the descending order of E. coli O157:H7, Salmonella , and L. monocytogenes . L. monocytogenes , the most UV-C-resistant strain, was then selected to test on frozen raspberries. The UV-C inactivation kinetic data of L. monocytogenes were well described using the Weibull equation. During 720 s of UV-C exposure, with a total dose of 7.8 × 102 mJ/cm2, a 1.5-log CFU/g reduction of L. monocytogenes population on the surface of frozen red raspberries was noted. No significant differences in total anthocyanins, total phenolics, and total antioxidant activity were observed between UV-C-treated and untreated frozen berries immediately after treatment. At the end of 9 months of storage at -35°C, UV-C-treated berries had statistically lower total phenolics, higher total anthocyanins, and similar total antioxidant activity compared with untreated berries. This study shows that UV-C light can be used to reduce the L. monocytogenes population on frozen raspberries.

Drug Release from Inert Spherical Matrix Systems Using Monte Carlo Simulations.

Computational approaches for predicting release properties from matrix devices have recently been purposed as an approach to better understand and predict such systems. The objective of this research is to study the behavior of drug delivery from inert spherical matrix systems of different size by means of computer simulation. To simulate the matrix medium, a simple cubic lattice was used, which was sectioned to make a spherical macroscopic system. The sites within the system were randomly occupied by drug-particles or excipient-particles in accordance with chosen drug/excipient ratios. Then, the drug was released from the matrix system simulating a diffusion process. When the released fraction was processed until 90% release, the Weibull equation suitably expressed the release profiles. On the basis of the analysis of release equations, it was found that close to the percolation threshold an anomalous released occurs, while in the systems with an initial drug load greater than 0.45, the released was Fickian type. It was also possible to determine the amount of drug trapped in the matrix, which was found to be a function of the initial drug load. The relationship between the two mentioned variables was adequately described by a model that involves the error function. Based on the these results and by means of a non-linear regression to the previous model, it was possible to determine the drug percolation threshold in these matrix devices. It was found that the percolation threshold is consistent with the value predicted by the percolation theory.

A Simplified Method for Analyzing the Fatigue life of a FPSO Mooring System

This paper deals with problems in connection with the evaluation of fatigue damage for mooring lines. Fatigue of the mooring system of ship-shaped FPSO units is assed here. The main objective of this paper is to find a new method for estimating the fatigue life with relatively simpler and less time consuming method, but without compromising accuracy. Using this method, it will be possible to check whether the mooring systems satisfy fatigue limit state (FLS) design criteria, especially for FPSO and also for MODUs which are usually not designed against fatigue. It will also give an idea whether a detail fatigue analysis is needed or not. In this method, the approximate fatigue damage of mooring line will be calculated from Weibull equation. But the challenge is to find the appropriate Weibull parameter, (h) value which will give the accurate fatigue damage. After conducting a study it is found that, using the Weibull parameter (h) value of 0.559 for windward line and 0.575 for leeward line; it might be possible to estimate the fatigue damage using the proposed simplified method. Information from the ultimate limit state (ULS) design results and the long term distribution of line tensions will also be used here. Since all FPSOs are designed based on ULS condition, all these information are available beforehand. Therefore, it will reduce the time required for fatigue calculation.

Influence of Hydrophilic Polymers on theβFactor in Weibull Equation Applied to the Release Kinetics of a Biologically Active Complex ofAesculus hippocastanum

Triterpenoid saponins complex of biological origin, escin, exhibits significant clinical activity in chronic venous insufficiency, skin inflammation, epidermal abrasions, allergic dermatitis, and acute impact injuries, especially in topical application. The aim of the study is the comparison of various hydrogel formulations, as carriers for a horse chestnut seed extract (EH). Methylcellulose (MC), two polyacrylic acid derivatives (PA1 and PA2), and polyacrylate crosspolymer 11 (PC-11) were employed. The release rates of EH were examined and a comparison with the Weibull model equation was performed. Application of MC as the carrier in the hydrogel preparation resulted in fast release rate of EH, whereas in the case of the hydrogel composed with PC-11 the release was rather prolonged. Applied Weibull function adhered best to the experimental data. Due to the evaluated shape parameterβ, in the Weibull equation, the systems under study released the active compound according to the Fickian diffusion.

Cationic nioplexes-in-polysaccharide-based hydrogels as versatile biodegradable hybrid materials to deliver nucleic acids.

Two polysaccharide-based hydrogels made of only κ-carrageenan (4%; w/v) or of a mixture of methylcellulose:κ-carrageenan (2%; w/v) were used to encapsulate cationic nioplexes. These vesicular particles were made of a synthetic aminolipid and polysorbate-80 (Tween-80), as a non-ionic surfactant agent. According to oscillatory rheological measurements, the presence of nioplexes did not compromise the mechanical integrity of the gels. In vitro niosomal release experiments demonstrated the liberation of nioplexes up to 24 h, and the curves were fitted according to Higuchi, Korsmeyer-Peppas and Weibull equation models, which indicated Fickian-diffusion controlled mechanisms. Besides nioplexes, cervical cancer cells were also entrapped within the biohydrogels. Cell release confirmed that these materials did not affect the cell viability, allowing cells to spread and proliferate after 24 h. The applicability of these biocompatible hydrogels was also extended to gene delivery. In this regard, the best silencing activities were found when cationic niosomes were complexed with antisense oligonucleotides in KC hydrogels. Nioplexes were able to release through the hydrogel and promoted silencing of luciferase expression in the presence of serum without using commercially available cationic lipids. Overall, the formation of such hybrid materials by integrating cationic nioplexes within biodegradable hydrogels provides a new perspective for the delivery of macromolecular therapeutics.

Modeling the fragmentation of rock grains using computed tomography and combined FDEM

The fracture and fragmentation of rock grains is attracting increasingly more research attention because it is relevant to today's challenges with particle raw materials. To contribute to understanding the fracture mechanisms of rock grains, the combined finite and discrete element method (FDEM) is adopted to simulate realistically shaped rock grains under single particle axial compression. Two groups of rock grains with different shape characteristics are considered to study their fracture processes under axial compression. Detained information of grain morphology was obtained using computed tomography (CT). The initial microstructure or heterogeneity within each rock grain is represented by a random distribution of the strength threshold. The influences of grain morphology on fragmentation patterns and fragmentation size distributions are systematically investigated. The results reveal that the dominant fracture mechanisms are related to the grain morphology. The more complex the grain shape, the more variable are the fracture patterns deviating from simple vertical splitting. Weibull statistics of grain crushing strength demonstrate that angular grains are characterized by both smaller characteristic strength and smaller Weibull modulus compared to those of rounded grains. This finding suggests that the crushing strength of angular grains may exhibit a more significant size hardening effect. The two-parameter Weibull equation can be used to fit the fragment size distribution, and the knowledge of the two fitting parameters is helpful for assessing the extent of fragmentation. The fragments of both angular and rounded grains satisfy the fractal distribution, and the fractal dimension narrowly distributes around 1.86±0.16 irrespective of the initial morphology, which is close to the exponent τ of the analytical predication of the fragment size distribution results from merged crack branches in three dimensions, where τ≈1.67.

Combined effect of high hydrostatic pressure (HHP) and antimicrobial from agro-industrial by-products against S. Typhimurium

The inactivation potential of HHP treatment (200 MPa-2 min) was evaluated against Salmonella enterica serovar Typhimurium in cauliflower and mandarin by-product infusions at 37 and 10 °C. By-product infusions exerted a strong antimicrobial effect used alone, achieving 5 log cycles of bacterial reduction for cauliflower by-product infusion after 10 h and for mandarin by-product infusion after 80 h, at 37 °C. The HHP treatment caused only one log cycle of cellular damage, but when inoculated cauliflower or mandarin by-product infusions were subjected to HHP treatment the antimicrobial effect against S. Typhimurium was enhanced, achieving 5 log cycles of inactivation in 6 h at 37 °C in both cases. Inactivation curves were adjusted to the Weibull equation and the kinetic parameters (b and n) were obtained. When HHP treatment was combined with by-product infusions, the inactivation rates were greater than when either of the by-product infusions was added separately. In conclusion, a synergistic antimicrobial effect against S. Typhimurium appeared to take place when HHP treatment was combined with cauliflower or mandarin by-product infusion. These infusions could be considered as an additional microbial control measure to guarantee the food safety and food quality of pasteurized food products that are stored under refrigeration.

Direct Exposure of Wheat Seeds to High-Voltage Electrostatic Fields Adversely Affects the Performance ofSitobion avenae(Hemiptera: Aphididae)

Exposing seeds to a high-voltage electrostatic field (HVEF) may influence the performance of herbivores and improve the germination rate by inducing biological and physiological changes in plants. In the current study, an age-stage, two-sex life table was established to evaluate the effects from directly exposing seeds to HVEFs on the performance of apterous Sitobion avenae (Fabricius) reared on winter wheat. We treated the wheat seeds by exposing them to an HVEF for 20 min at three intensities: 2, 4, or 6 KV/cm. Controls received no treatment (0 KV/cm). The results indicated that the parameters of the net reproductive rate (R0), the intrinsic rate of increase (r), and the mean generation span (T) of S. avenae were significantly reduced by HVEFs through multiple generations. In addition, the age-specific survival rate (lx) and comparison with the results of a Weibull equation analysis suggested that S. avenae had the shortest life span when seeds were exposed to an HVEF at 4 KV/cm. Overall, these findings indicated that direct exposure of wheat seeds to an HVEF at 4 KV/cm could adversely affect the performance of S. avenae.

Estimation of time-varying discharge and cumulative volume in individual overtopping waves

The time variation of discharge per unit dike length in an overtopping wave is characterized by a rapid increase to a maximum discharge that can be several times greater than the mean discharge, followed by a slower decrease in discharge until overtopping for that wave ceases. Measurements of wave overtopping acquired during the European small-scale FlowDike experiments were analyzed to identify individual overtopping waves using a two-step “supervised” procedure that combines the best features of automated wave determination augmented with manual error correction and validation. The result was a well-vetted data set of 5799 individual overtopping waves represented by time-series of flow depth and velocity near the seaward edge of the dike crest. The model dikes had planar seaward dike slopes of either 1V-on-3H or 1V-on-6H. Instantaneous discharge time series were calculated as the product of the flow thickness and velocity time series. In this paper, the two-parameter Weibull probability density function is adopted to represent the time variation of instantaneous discharge in an overtopping wave. Values of the Weibull scale factors, a, and shape factors, b, are obtained through nonlinear best-fitting of the Weibull equation to all 5799 waves. Best fits were also performed for the simpler Rayleigh version of the Weibull equation when b=2. An empirical equation was developed for scale factor, a, in terms of predicable parameters of the overtopping waves. The shape factor, b, could not be successfully parameterized, but it was found that the shape factors are narrowly distributed about the Rayleigh value of b=2. Predictions of time-varying discharge made using the Weibull equation with b=2 (i.e., Rayleigh equation) are assessed in terms of the root-mean-square errors between predictions and measurements. The estimates are reasonable for most of the waves. The capability to estimate the time-varying discharge in individual overtopping waves will improve the art of full-scale wave overtopping simulation, and the resulting empirical equations will contribute to methodologies aimed at quantifying the resiliency of dike erosion protection.

Oviposition Model of Ephestia kuehniella (Lepidoptera: Pyralidae).

In this study, we examined the fecundity, survival, and adult longevity of Ephestia kuehniella (Zeller) at different temperatures (15, 17.5, 20, 22.5, 25, 27.5, and 30 °C), and developed a model of oviposition. The fecundity, survival, and adult longevity of E. kuehniella were affected by temperature. Longevity reduced from 15.7 d at 15 °C to 8.79 d at 30 °C. Total fecundity was lowest (160.54 eggs) at 30 °C and highest (351.75 eggs) at 25 °C. The relationship between temperature and total fecundity was described by a nonlinear function. Cumulative age-specific egg laying fitted well to the two-parameter Weibull equation and survival of adults fitted well to a reverse logistic curve. These three temperature-dependent attributes (age-specific cumulative egg laying, temperature-dependent total fecundity, and age-specific survival rate) were integrated into a model of oviposition. Simulation of oviposition using the model has the potential to be useful for predicting patterns of occurrence of E. kuehniella egg populations in stores.

Kinetics on the turbidity change of wheat starch during its retrogradation.

Wheat starch dispersions of 10-40% (w/w) were gelatinized and the change in turbidity of each solution during storage was measured in the 400-1100nm wavelength range. The relative transmittance, defined as the ratio of transmittance at any storage time to that at the initial time, decreased when the solutions were stored at 5 and 30°C; the decrease, reflecting the progress of retrogradation, was larger at 5°C than at 30°C. Most of the changes in relative transmission taking place over 14days were achieved during the first 90min. The change in the relative transmittance is inversely proportional to the energy required for deformation. The kinetics on change in relative transmittance can be expressed by Weibull equation. The larger rate constant at higher starch concentration could be ascribed to the state of the starch granules, which depended on starch concentration.

Effects of inulin, fructooligosaccharides/glucose and pH on the shape of the death kinetic of Lactobacillus reuteriDSM 20016

SummaryThe viability of Lactobacillus reuteri, Lb. delbrueckii subsp. bulgaricus and Lb. paracasei was assessed in a laboratory medium containing inulin (5 g L−1) or glucose + FOS (fructooligosaccharides) (2.5 + 2.5 g L−1). Data were modelled through the Weibull equation pinpointing that prebiotics determined a decrease in the shape parameter. In the 2nd step, L. reuteri was used as the test microorganism; pH, storage temperature and the amounts of FOS + glucose and inulin were combined through a 4‐variable/5‐level central composite design. Temperature, pH and glucose + FOS affected the microbiological shelf life; inulin was not significant. The maximum value of shelf life was found at pH 8.5 and with 5.0 g L−1 of glucose + FOS. The combination of pH and prebiotics affected the shape parameter with a shift from a convex to a concave trend and vice versa: their effect was different depending on the use of a single prebiotic or a mix.

Failure mechanisms of Al2O3 with different glass phase content at cryogenic temperatures

The effects of glass phase and temperature on the mechanical properties of 99%, 92%, 85% and 75% Al2O3 are investigated. The in-situ XRD results revealed that the lattice constants of Al2O3 single crystals were reduced when temperature decreased from room temperature (RT) to 30K. The results of mechanical properties were analyzed by Weibull equation. It can be concluded that for the samples containing same content of glass phase, the bending strength and fracture toughness increased as temperature decreased from RT to 77K. While at the same test temperature, the mechanical properties degraded when the glass phase content increased. The statistical analysis of indentation crack propagation paths of 99% Al2O3 indicated that the proportion of transgranular fracture was increased at 77K.

Fracture strength and principal stress fields during crush testing of the SiC layer in TRISO-coated fuel particles

Diametrical compression testing is an important technique to evaluate fracture properties of the SiC layer in TRISO-coated nuclear fuel particles. This study was conducted to expand the understanding and improve the methodology of the test. An analytic solution and multiple FEA models are used to determine the development of the principal stress fields in the SiC shell during a crush test. An ideal fracture condition where the diametrical compression test best mimics in-service internal pressurization conditions was discovered. For a small set of empirical data points, results from different analysis methodologies were input to an iterative Weibull equation set to determine characteristic strength (332.9 MPa) and Weibull modulus (3.80). These results correlate well with published research. It is shown that SiC shell asphericity is currently the limiting factor of greatest concern to obtaining repeatable results. Improvements to the FEA are the only apparent method for incorporating asphericity and improving accuracy.