Lecture notes on probability, statistics, and experimental errors; an elementary summary for students of experimental science.

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Experimental alternatives for evaluation of progenies and clones in eucalyptus breeding programs

The feasibility of using augmented block designs and spatial analysis methods for early stage selection in eucalyptus breeding programs was tested. A total of 113 half-sib progenies of Eucalyptus urophylla and eight clones were evaluated in an 11 x 11 triple lattice experiment at two locations: Posto da Mata (Bahia, Brazil) and São Mateus (Minas Gerais, Brazil). Four checks were randomly allocated within each block. Plots consisted of 15 m long rows containing 6 plants spaced 3 m apart. The girth at breast height (cm/plant) was evaluated at 19 and 26 months of age. Variance analyses were performed according to the following methods: lattice design, randomized complete block design, augmented block design, Papadakis method, moving means method, and check plots. Comparisons among different methods were based on the magnitude of experimental errors and precision of the estimates of genetic and phenotypic parameters. General results indicated that augmented block design is useful to evaluate progenies and clones in early selection in eucalyptus breeding programs using moderate and low selection intensities. However, this design is not suitable for estimating genetic and phenotypic parameters due to its low precision. Check plots, nearest neighbour, Papadakis (1937), and moving means methods were efficient in removing the heterogeneity within blocks. These efficiencies were compared to that in lattice analysis for estimation of genetic and phenotypic parameters.

An experimental verification of newton's second law

We describe an experimental procedure to probe the validity of Newton's second law. The experimental arrangement allows us to accelerate a glider on an air track by means of forces that are both steady and known. We also show how to determine acceleration from average speeds calculated for successive time intervals of the motion measured by using several electronic counters connected to a single-crystal oscillator circuit. Within experimental errors, the experiments clearly show the proportionality between acceleration and force for a fixed mass and between acceleration and inverse of mass for a fixed force. © by the Sociedade Brasileira de Física.

Transducer for direct measurement of skin friction in hypervelocity impulse facilities

An acceleration compensated transducer was developed to enable the direct measurement of skin friction in hypervelocity impulse facilities. The gauge incorporated a measurement and acceleration element that employed direct shear of a piezoelectric ceramic. The design integrated techniques to maximize rise time and shear response while minimizing the affects of acceleration, pressure, heat transfer, and electrical interference. The arrangement resulted in a transducer natural frequency near 40 kHz. The transducer was calibrated for shear and acceleration in separate bench tests and was calibrated for pressure within an impulse facility. Uncertainty analyses identified only small experimental errors in the shear and acceleration calibration techniques. Although significant errors were revealed in the method of pressure calibration, total skin-friction measurement errors as low as +/-7-12% were established. The transducer was successfully utilized in a shock tunnel, and sample measurements are presented for flow conditions that simulate a flight Mach number near 8.

Leaf water potential and osmotic adjustment as physiological traits to improve drought tolerance in rice

A sample of recombinant inbred lines (RILs) was derived from a bi-parental cross between Lemont and BK88-BR6, which contrasted in maintenance of leaf water potential (LWP) and expression of osmotic adjustment (OA). Genotypic variation for LWP and OA, and their associations with yield determination under water deficit, was studied in a series of five field experiments. Genotypic variation in the maintenance of high LWP was consistent across water deficit experiments. In the determination of genotypic variation in the maintenance of LWP, rate of water deficit was not an important factor influencing ranking, but degree of water deficit, and phenological development stage were important, particularly around heading. Genotypic variation in expression of OA was also observed under water deficits during both vegetative and flowering stages but ranking was inconsistent across experiments. This was in part because of large experimental errors associated with its measurement, but also because the expression of OA was associated with extent of decline of LWP. The relationship between OA and LWP was demonstrated when data were combined across experiments for vegetative and flowering stages. Under water-limited conditions around flowering, grain yield reduction was mainly due to a increased spikelet sterility. Variation in OA was not related to grain yield nor yield components. There were however, negative phenotypic and genetic correlations between LWP and percentage spikelet sterility measured at flowering stage on panicles at the same development stage during a water deficit treatment. This suggests that traits contributing to the maintenance of high LWP minimized the effects of water deficit on spikelet sterility and consequently grain yield. (C) 2002 Elsevier Science B.V. All rights reserved.

A comparison between joint coordinate system and attitude vector for multi-segment foot kinematics.

The joint angles of multi-segment foot models have been primarily described using two mathematical methods: the joint coordinate system and the attitude vector. This study aimed to determine whether the angles obtained through these two descriptors are comparable, and whether these descriptors have similar sensitivity to experimental errors. Six subjects walked eight times on an instrumented walkway while the joint angles among shank, hindfoot, medial forefoot, and lateral forefoot were measured. The angles obtained using both descriptors and their sensitivity to experimental errors were compared. There was no overall significant difference between the ranges of motion obtained using both descriptors. However, median differences of more than 6° were noticed for the medial-lateral forefoot joint. For all joints and rotation planes, both descriptors provided highly similar angle patterns (median correlation coefficient: R>0.90), except for the medial-lateral forefoot angle in the transverse plane (median R=0.77). The joint coordinate system was significantly more sensitive to anatomical landmarks misplacement errors. However, the absolute differences of sensitivity were small relative to the joints ranges of motion. In conclusion, the angles obtained using these two descriptors were not identical, but were similar for at least the shank-hindfoot and hindfoot-medial forefoot joints. Therefore, the angle comparison across descriptors is possible for these two joints. Comparison should be done more carefully for the medial-lateral forefoot joint. Moreover, despite different sensitivities to experimental errors, the effects of the experimental errors on the angles were small for both descriptors suggesting that both descriptors can be considered for multi-segment foot models.

Fertilizer 15N balance in a coffee cropping system: a case study in Brazil

Knowledge about the fate of fertilizer nitrogen in agricultural systems is essential for the improvement of management practices in order to maximize nitrogen (N) recovery by the crop and reduce N losses from the system to a minimum. This study involves fertilizer management practices using the 15N isotope label applied in a single rate to determine the fertilizer-N balance in a particular soil-coffee-atmosphere system and to deepen the understanding of N plant dynamics. Five replicates consisting of plots of about 120 plants each were randomly defined within a 0.2 ha coffee plantation planted in 2001, in Piracicaba, SP, Brazil. Nine plants of each plot were separated in sub-plots for the 15N balance studies and treated with N rates of 280 and 350 kg ha-1 during 2003/2004 and 2004/2005, respectively, both of them as ammonium sulfate enriched to a 15N abundance of 2.072 atom %. Plant shoots were considered as separate parts: the orthotropic central branch, productive branches, leaves of productive branches, vegetative branches, leaves of vegetative branches and fruit. Litter, consisting of dead leaves accumulated below the plant canopy, was measured by the difference between leaves at harvest and at the beginning of the following flowering. Roots and soil were sampled down to a depth of 1.0 at intervals of 0.2 m. Samples from the isotopic sub-plots were used to evaluate total N and 15N, and plants outside sub-plots were used to evaluate dry matter. Volatilization losses of NH3 were estimated using special collectors. Leaching of fertilizer-N was estimated from deep drainage water fluxes and 15N concentrations of the soil solution at 1 m soil depth. At the end of the 2-year evaluation, the recovery of 15N applied as ammonium sulfate was 19.1 % in aerial plant parts, 9.4 % in the roots, 23.8 % in the litter, 26.3 % in the fruit and 12.6 % remaining in the 0_1.0 m soil profile. Annual leaching and volatilization losses were very small (2.0 % and 0.9 %, respectively). After two years, only 6.2 % N were missing in the balance (100 %) which can be attributed to other non-estimated compartments and experimental errors. Results show that an enrichment of only 2 % atom 15N allows the study of the partition of fertilizer-N in a perennial crop such as coffee during a period of two years.

Elastic constants of Ni-Mn-Ga magnetic shape memory alloys

We have measured the adiabatic second order elastic constants of two Ni-Mn-Ga magnetic shape memory crystals with different martensitic transition temperatures, using ultrasonic methods. The temperature dependence of the elastic constants has been followed across the ferromagnetic transition and down to the martensitic transition temperature. Within experimental errors no noticeable change in any of the elastic constants has been observed at the Curie point. The temperature dependence of the shear elastic constant C' has been found to be very different for the two alloys. Such a different behavior is in agreement with recent theoretical predictions for systems undergoing multi-stage structural transitions.

Segmentation of foot and ankle complex based on kinematic criteria.

Although various foot models were proposed for kinematics assessment using skin makers, no objective justification exists for the foot segmentations. This study proposed objective kinematic criteria to define which foot joints are relevant (dominant) in skin markers assessments. Among the studied joints, shank-hindfoot, hindfoot-midfoot and medial-lateral forefoot joints were found to have larger mobility than flexibility of their neighbour bonesets. The amplitude and pattern consistency of these joint angles confirmed their dominancy. Nevertheless, the consistency of the medial-lateral forefoot joint amplitude was lower. These three joints also showed acceptable sensibility to experimental errors which supported their dominancy. This study concluded that to be reliable for assessments using skin markers, the foot and ankle complex could be divided into shank, hindfoot, medial forefoot, lateral forefoot and toes. Kinematics of foot models with more segments must be more cautiously used.

Alkali Content of Fly Ash – Measuring and Testing Strategies for Compliance, TR-628, 2015

Sodium and potassium are the common alkalis present in fly ash. Excessive amounts of fly ash alkalis can cause efflorescence problems in concrete products and raise concern about the effectiveness of the fly ash to mitigate alkali-silica reaction (ASR). The available alkali test, which is commonly used to measure fly ash alkali, takes approximately 35 days for execution and reporting. Hence, in many instances the fly ash has already been incorporated into concrete before the test results are available. This complicates the job of the fly ash marketing agencies and it leads to disputes with fly ash users who often are concerned with accepting projects that contain materials that fail to meet specification limits. The research project consisted of a lab study and a field study. The lab study focused on the available alkali test and how fly ash alkali content impacts common performance tests (mortar-bar expansion tests). Twenty-one fly ash samples were evaluated during the testing. The field study focused on the inspection and testing of selected, well documented pavement sites that contained moderately reactive fine aggregate and high-alkali fly ash. A total of nine pavement sites were evaluated. Two of the sites were control sites that did not contain fly ash. The results of the lab study indicated that the available alkali test is prone to experimental errors that cause poor agreement between testing labs. A strong (linear) relationship was observed between available alkali content and total alkali content of Class C fly ash. This relationship can be used to provide a quicker, more precise method of estimating the available alkali content. The results of the field study failed to link the use of high-alkali fly ash with the occurrence of ASR in the various concrete sites. Petrographic examination of the pavement cores indicated that Wayland sand is an ASR-sensitive aggregate. This was in good agreement with Iowa DOT field service records. It was recommended that preventative measures should be used when this source of sand is used in concrete mixtures.

A priori parameterisation of the CERES soil-crop models and tests against several European data sets

Mechanistic soil-crop models have become indispensable tools to investigate the effect of management practices on the productivity or environmental impacts of arable crops. Ideally these models may claim to be universally applicable because they simulate the major processes governing the fate of inputs such as fertiliser nitrogen or pesticides. However, because they deal with complex systems and uncertain phenomena, site-specific calibration is usually a prerequisite to ensure their predictions are realistic. This statement implies that some experimental knowledge on the system to be simulated should be available prior to any modelling attempt, and raises a tremendous limitation to practical applications of models. Because the demand for more general simulation results is high, modellers have nevertheless taken the bold step of extrapolating a model tested within a limited sample of real conditions to a much larger domain. While methodological questions are often disregarded in this extrapolation process, they are specifically addressed in this paper, and in particular the issue of models a priori parameterisation. We thus implemented and tested a standard procedure to parameterize the soil components of a modified version of the CERES models. The procedure converts routinely-available soil properties into functional characteristics by means of pedo-transfer functions. The resulting predictions of soil water and nitrogen dynamics, as well as crop biomass, nitrogen content and leaf area index were compared to observations from trials conducted in five locations across Europe (southern Italy, northern Spain, northern France and northern Germany). In three cases, the model’s performance was judged acceptable when compared to experimental errors on the measurements, based on a test of the model’s root mean squared error (RMSE). Significant deviations between observations and model outputs were however noted in all sites, and could be ascribed to various model routines. In decreasing importance, these were: water balance, the turnover of soil organic matter, and crop N uptake. A better match to field observations could therefore be achieved by visually adjusting related parameters, such as field-capacity water content or the size of soil microbial biomass. As a result, model predictions fell within the measurement errors in all sites for most variables, and the model’s RMSE was within the range of published values for similar tests. We conclude that the proposed a priori method yields acceptable simulations with only a 50% probability, a figure which may be greatly increased through a posteriori calibration. Modellers should thus exercise caution when extrapolating their models to a large sample of pedo-climatic conditions for which they have only limited information.

Datação da fração humina da matéria orgânica do solo e sua comparação com idades 14C de carvões fósseis

The radiocarbon dating of the soil organic matter (SOM) is a polemic subject, due mainly to the complexity of the formation of the soils and to the variable contamination from several sources. Soil samples from 4 different Brazilian localities were submitted to physical and chemical pre-treatment for the extraction of humin fraction, which is the most stable organic compound and theoretically the oldest and representative of the age of the SOM. The radiocarbon dating obtained from the total SOM and their humin fractions are compared to the 14C ages from buried charcoals at similar depths. The radiocarbon ages obtained from such charcoals are, in most of the cases, concordant within the experimental errors of those obtained on humin fractions, or are in average 10% higher, with one exception. Thus, the ages on humin fractions could be assumed as the minimum ages for the associated soils, while the results obtained on total SOM, even at depths until 200 cm, exhibit pronounced contamination effect by modern carbon, rejuvenating their ages.

Comparação entre métodos de quantificação em cromatografia gasosa: um experimento para cursos de química

This article describes an experiment designed to teach quantitative determination in gas chromatography (GC) in Organic and Analytical Chemistry practical classes. The experiment consisted of extracting and analyzing eugenol from clove seeds to perform a quantitative approach aimed at comparing results obtained by external and internal calibration procedures. Therefore, this experiment proved to be very effective tool to enhance students awareness on the need to understand different types of calibration in GC and on how to avoid common experimental errors, and to find the best ways to eliminate their interference during the quantitative analysis phase.

Methane combustion kinetic rate constants determination: an ill-posed inverse problem analysis

Methane combustion was studied by the Westbrook and Dryer model. This well-established simplified mechanism is very useful in combustion science, for computational effort can be notably reduced. In the inversion procedure to be studied, rate constants are obtained from [CO] concentration data. However, when inherent experimental errors in chemical concentrations are considered, an ill-conditioned inverse problem must be solved for which appropriate mathematical algorithms are needed. A recurrent neural network was chosen due to its numerical stability and robustness. The proposed methodology was compared against Simplex and Levenberg-Marquardt, the most used methods for optimization problems.

Elastic constants of Ni-Mn-Ga magnetic shape memory alloys

We have measured the adiabatic second order elastic constants of two Ni-Mn-Ga magnetic shape memory crystals with different martensitic transition temperatures, using ultrasonic methods. The temperature dependence of the elastic constants has been followed across the ferromagnetic transition and down to the martensitic transition temperature. Within experimental errors no noticeable change in any of the elastic constants has been observed at the Curie point. The temperature dependence of the shear elastic constant C' has been found to be very different for the two alloys. Such a different behavior is in agreement with recent theoretical predictions for systems undergoing multi-stage structural transitions.