Rice Method Research Articles

Experimental validation of a topological derivative-based crack growth control method using digital image correlation

PurposeThe purpose of this paper is to experimentally validate the crack growth control based on the topological derivative of the famous Rice's integral.Design/methodology/approachSingle edge notch tensile specimens with two configurations were tested. Displacement fields near notch were experimentally obtained using the digital image correlation method. These displacements were used to verify the minimization of the associated shape functional, which is defined in terms of the Rice's integral, when a set of controls (holes) positioned according to the topological derivative information, is inserted. Based on the Griffth's energy criterion, this minimization represents an improvement in the fracture toughness of cracked bodies.FindingsThe experimental tests confirmed that a decrease around 27% in the value of the associated shape functional can be obtained following this approach. Therefore, the results allow us to conclude that the predictive methodology for crack growth control based on the topological derivative is feasible.Originality/valueThis is the first work concerning experimental validation of crack growth control based on the topological derivative method.

Towards a Realistic Analysis of the QuickSelect Algorithm

We revisit the analysis of the classical QuickSelect algorithm. Usually, the analysis deals with the mean number of key comparisons, but here we view keys as words produced by a source, and words are compared via their symbols in lexicographic order. Our probabilistic models belong to a broad category of information sources that encompasses memoryless (i.e., independent-symbols) and Markov sources, as well as many unbounded-correlation sources. The realistic cost of the algorithm is here the total number of symbol comparisons performed by the algorithm, and, in this context, the average-case analysis aims to provide estimates for the mean number of symbol comparisons. For the QuickSort algorithm, known average-case complexity results are of ?(nlogn)${\Theta } (n \log n)$ in the case of key comparisons, and ?(nlog2n)${\Theta }(n\log ^{2} n)$ for symbol comparisons. For QuickSelect algorithms, and with respect to key comparisons, the average-case complexity is ?(n). In this present article, we prove that, with respect to symbol comparisons, QuickSelect's average-case complexity remains ?(n). In each case, we provide explicit expressions for the dominant constants, closely related to the probabilistic behaviour of the source. We began investigating this research topic with Philippe Flajolet, and the short version of the present paper (the ICALP'2009 paper) was written with him. As usual, Philippe played a central role, notably on the following points: introduction of theQuickValalgorithm, tameness of sources, and use of Rice's method. He also made many experiments exhibiting the asymptotic slope ?(?) and plotted nice graphs, which are reproduced in this paper. Even though the extended abstract does not provide any proof of the analysis of the algorithmQuickQuant, Philippe also devised with us a precise plan for this proof which has now completely been written. For all these reasons, we could have added (and certainly would have liked to add) Philippe as a co-author of this paper. On the other hand, Philippe was extremely exacting of how his papers were to be written and organised, and we cannot be sure that he would have liked or validated our editing choices. In the end, this is why we have decided not to include him as a co-author, but instead, to dedicate, with deference and affection, this paper to his memory. Thank you, Philippe!

Estimation of Extreme Ship Response

In practice the severity of ship response is measured by high quantiles of long-term distribution of the response. The distribution is estimated by combining the short-term distribution of the response with a long-term probability distribution of encountered sea states. The paper describes an alternative approach, the so-called Rice's method, based on estimation of expected number of upcrossings of high levels by stress during 1 year. The method requires description of long-term variability of the standard deviation, skewness, kurtosis, and zero upcrossing frequency of ship response. It is assumed that the parameters are functions of encountered significant wave height, heading angle, and ship speed. The relation can be estimated from the measured stresses or computed by dedicated software assuming rigid ship hull model. Then Winterstein's transformed Gaussian model is used to estimate the upcrossing rates of response during a sea state. The proposed method is validated using the full-scale measurements of a 2,800 TEU container ship during the first 6 months of 2008. Numerical estimation of 4,400 TEU container ship extreme of the extreme response for a 4400 TEU container ship illustrates the approach when no measurements are available.

Digital search trees with m trees: Level polynomials and insertion costs

Analysis of Algorithms We adapt a novel idea of Cichon's related to Approximate Counting to the present instance of Digital Search Trees, by using m (instead of one) such trees. We investigate the level polynomials, which have as coefficients the expected numbers of data on a given level, and the insertion costs. The level polynomials can be precisely described, thanks to formulae from q-analysis. The asymptotics of expectation and variance of the insertion cost are fairly standard these days and done with Rice's method.

Asymptotic Properties of a Leader Election Algorithm

We consider a serialized coin-tossing leader election algorithm that proceeds in rounds until a winner is chosen, or all contestants are eliminated. The analysis allows for either biased or fair coins. We find the exact distribution for the duration of any fixed contestant; asymptotically, it turns out to be a geometric distribution. Rice's method (an analytic technique) shows that the moments of the duration contain oscillations, which we give explicitly for the mean and variance. We also use convergence in the Wasserstein metric space to show that the distribution of the total number of coin flips (among all participants), suitably normalized, approaches a normal limiting random variable.

Asymptotic Properties of a Leader Election Algorithm

We consider a serialized coin-tossing leader election algorithm that proceeds in rounds until a winner is chosen, or all contestants are eliminated. The analysis allows for either biased or fair coins. We find the exact distribution for the duration of any fixed contestant; asymptotically, it turns out to be a geometric distribution. Rice's method (an analytic technique) shows that the moments of the duration contain oscillations, which we give explicitly for the mean and variance. We also use convergence in the Wasserstein metric space to show that the distribution of the total number of coin flips (among all participants), suitably normalized, approaches a normal limiting random variable.

Effects of hyperbaric oxygen on the activation of β-catenin in hypoxic ischemic neonate rats

Objective To explore the relationship between the proliferation of neural stem cells (NSCs)and the expression of β-catenin protein in neonate rats with hypoxic ischemic brain damage (HIBD) after hyperbaric oxygen (HBO) therapy. Methods One hundred and eighty Sprague-Dawley rats aged 7 days were randomly divided into a normal control group (CON) , a HIBD model group and a HBO treatment group. The HIBD model was induced using Rice's method. Beginning 3h after the HIBD, HBO was administered to the HBO treatment group at 2 atmospheres for 60 min, once daily for 7 days. The HIBD model group was not given any treatment. The expression of nestin/β-catenin protein in the subventricular zone of the ischemic brain was double-stained for immunofluorescence and analyzed by confocal scanning microscopy dynamically at 3 hours, 21 hours, and then on the 3rd, 5th, 7th and 14th day of HBO therapy. The expression of whole cell β-catenin and nuclear β-catenin protein in the left brain were also examined by Western blotting at these 6 time points. Linear correlation was used to analyze the correlation between β-catenin and nestin protein. Results The expression of β-catenin protein in NSCs increased initially at the 21st hour after HBO therapy in the model group and the HBO group as compared with the normal control group.β-catenin protein in the model group reached a higher level, though there was no significant difference between model group and the HBO group. At the 5th day of HBO therapy β-catenin protein in the HBO group had reached a significantly higher level than in the model group. At the 14th day the average expression of β-catenin in the HBO group began to decrease. The expression of nestin protein began to increase 21 hours after HBO therapy began, and it peaked at the 7th day of HBO therapy and then decreased. In the HBO group the increase in nestin protein was linearly correlated with that of β-catenin protein. The whole cell β-catenin protein and β-catenin nucleic protein readings increased initially by the 21st hour of HBO therapy and by the 5th day were significantly higher than the levels in the model group. Conclusion HBO treatment is capable of stimulating the proliferation of NSCs in HIBD neonate rats.The proliferation of NSCs is correlated with the activation of β-catenin protein. Key words: Hyperbaric oxygen; Hypoxic-ischemic brain damage; Neural stem cells; β-catenin

Separation of the maxima in samples of geometric random variables

We consider samples of n geometric random variables W1 W2 ... Wn where P{W) = i} = pqi-l, for 1 ? j ? n, with p + q = 1. For each fixed integer d > 0, we study the probability that the distance between the consecutive maxima in these samples is at least d. We derive a probability generating function for such samples and from it we obtain an exact formula for the probability as a double sum. Using Rice's method we obtain asymptotic estimates for these probabilities. As a consequence of these results, we determine the average minimum separation of the maxima, in a sample of n geometric random variables with at least two maxima.

Early cognitive function of rats with ischemic hypoxic brain injury during the neonatal period

Objective To establish an early cognitive disorder model in rats and investigate the early cognitive functioning after ischemic hypoxic brain injury during the neonatal period. Methods Forty-six newborn Sprague-Dawley rats were randomized into a 21-d-old group and a 31-d-old group. These 2 groups were then subdivided into model and sham-operated subgroups (M21, n=12; SH21, n=11; M31, n=12; SH31, n=11). A model of neonatal early cognitive disorder was established in the rats of the M21 and M31 groups using a modification of Rice's method. Rats in the SH21 and SH31 groups received skin incisions and common carotid artery separation without ligation or hypoxia. Each group was tested with a Morris water maze. The rats were sacrificed after testing, and brain tissue was examined under the electron microscope. Nissl staining allowed Nissl body quantification and neurocyte acin the M21 group was significantly longer than in the SH21 group. The 31-d-old subgroups had shorter average escaping latencies than the corresponding 21-d-old subgroups. (b) Spatial memory: The average platform times, Ⅰ region times and Ⅰ region distances showed no significant differences among groups. ②Brain pathology (a) Gross appearance: Obvious ischemic hemisphere atrophy was observed in the M group, and no abnormality was observed in the SH group. (b) Electron microscopic observation: In the SH group cell ultrastructures in the ischemic hippocampus were normal. Karyopyknosis and dilated endoplasmic reticulums were found in the M group. More mitochondria were foundin the presynaptic membranes of the ischemic hippocampus in the M group than that in the SH group. (c) Nissl body quantification and neurocyte activity analysis: Significantly less activity in the ischemic cortex was found in the M21 group compared to the SH21 group. More activity was observed in the 31-d-old subgroups than in the corresponding21-d-old subgroups. Conclusions ①The neonatal rats with ischemic hypoxic brain injury had prolonged average escaping latency and depressed neuronal activity. ②The 31-d-old rats had better spatial localization learning ability than the 21-d-old rats. Key words: Early cognition; Ischemic hypoxic brain damage; Morris water maze; Neonatal rats

Experimental and Theoretical Investigations of Fatigue Crack Growth in D16 Alloy

Experimental and Theoretical Investigations of Fatigue Crack Growth in D16 AlloyIn this work the arising and development of fatigue crack in aluminium alloy D16, taking into consideration the influence of notch in the form of hole with incisions which were done on its sides were tested. The process of working out of tests' programme was preceded by numeric analysis of stresses pattern and strains distribution in the zone of notch's influence which was focused on determination of stresses' face values. To examine stress and strain distributions, the specialised FEM software (MSC. Patran and MSC. Nastran) was applied. Findings have been presented in the form of a statement of σmax and εmax values, and functions of the following factors: aσ, aε, and ak, computed on the grounds of these values for both different distances from the bottom of the notch and assumed levels of loading the specimens. Theoretical analysis has been supplemented with experimental investigation into the microstructure of fatigue-fracture surfaces in the area of crack initiation and that of fatigue of a propagating crack. The paper has been intended to present a model of the probabilistic estimation of fatigue life of structural members. The model has been based on the deterministic description of the cracking. Analyzed were components with notches in the form of centrally located holes with side cuts. In the method of probabilistically approaching the crack propagation, some dependences have been used that take account of the presence of areas showing plastic strains in front of crack tips. It has been assumed that the cracking can be modeled on the grounds of some general-purpose quantity used to describe the energy state in the area of the crack tip, i.e. the Rice's integral (J). The formulated computational model has been used to estimate fatigue life of model components made of D16 alloy. Experimental work was carried out using some flat specimens with centrally positioned holes. They were exposed to flat bending at R = 0. Analytical and experimental results have shown pretty good conformity.

Wplyw wybranych warunkow wtryskiwania na odpornosc na pekanie kompozytu polipropylenu z talkiem

The results of investigations of the effects of injection molding conditions on Rice's integral / values for the composites of polypropylene with 25wt. % of talc (PPH 25T) are presented. The specimens for tests were prepared by injection molding according to the schedule elaborated (Fig. 1-3, Table 1 and 2). Rice's integral was taken as a measure for crack resistance evaluation. Pareto analysis, enabling us to assume the effects of selected injection molding conditions (mold temperature, injection temperature and velocity, clamping pressure) on Rice's integral value, has been done (Fig. 4). It was found that mold temperature and injection temperature influence most the crack resistance of PPH 25T composite (Fig. 5-7).

The average position of the first maximum in a sample of geometric random variables

We consider samples of n geometric random variables $(Γ _1, Γ _2, \dots Γ _n)$ where $\mathbb{P}\{Γ _j=i\}=pq^{i-1}$, for $1≤j ≤n$, with $p+q=1$. The parameter we study is the position of the first occurrence of the maximum value in a such a sample. We derive a probability generating function for this position with which we compute the first two (factorial) moments. The asymptotic technique known as Rice's method then yields the main terms as well as the Fourier expansions of the fluctuating functions arising in the expected value and the variance.

A simple approach using Bouwer and Rice's method for slug test data analysis.

Slug test data obtained from tests performed in an unconfined aquifer are commonly analyzed by graphical or numerical approaches to determine the aquifer parameters. This paper derives three fourth-degree polynomials to represent the relationship between Bouwer and Rice's coefficients and the ratio of the screen length to the radius of the gravel envelope. A numerical approach using the nonlinear least squares and Newton's method is used to determine hydraulic conductivity from the best fit of the slug test data. The method of nonlinear least squares minimizes the sum of the squares of the differences between the predicted and observed water levels inside the well. With the polynomials, the hydraulic conductivity can be obtained by simply solving the nonlinear least squares equation by Newton's method. A computer code, SLUGBR, was developed from the derived polynomials using the proposed numerical approach. The results of analyzing two slug test datasets show that SLUGBR can determine hydraulic conductivity with very good accuracy.

Projections on spherical cones, maximum of Gaussian fields and Rice's method

Using Rice's method to obtain the distribution of the maximum of Gaussian random fields we give the distribution of the length of the projection of a Gaussian variable onto any convex or non-convex spherical cone.

Entropy computations via analytic depoissonization

We investigate the basic question of information theory, namely, evaluation of Shannon entropy, and a more general Renyi (1961) entropy, for some discrete distributions (e.g., binomial, negative binomial, etc.). We aim at establishing analytic methods (i.e., those in which complex analysis plays a pivotal role) for such computations which often yield estimates of unparalleled precision. The main analytic tool used here is that of analytic poissonization and depoissonization. We illustrate our approach on the entropy evaluation of the binomial distribution, that is, we prove that for binomial (n, p) distribution Shannon's h/sub n/ becomes h/sub n//spl ap/ 1/2 ln n+ 1/2 +ln/spl radic/(2/spl pi/p(1-p))+/spl Sigma//sub k/spl ges/1/a/sub k/n/sup -k/ where a/sub k/ are explicitly computable constants. Moreover, we argue that analytic methods (e.g., complex asymptotics such as Rice's method and singularity analysis, Mellin transforms, poissonization, and depoissonization) can offer new tools for information theory, especially for studying second-order asymptotics (e.g., redundancy). In fact, there has been a resurgence of interest and a few successful applications of analytic methods to a variety of problems of information theory, therefore, we propose to name such investigations as analytic information theory.

Analyses of Slug Tests and Hydraulic Conductivity Variations in the Near Field of a Two‐Well Tracer Experiment Site

AbstractThree‐hundred eight slug tests were conducted in a 5 × 5 m area in a coastal, sandy aquifer at the Georgetown site in South Carolina to characterize three‐dimensional aquifer heterogeneity. Methods developed by Hvorslev, Bouwer and Rice, and Cooper et al. were employed to estimate hydraulic conductivity values from the slug test data. These three methods produced similar spatial distributions of the hydraulic conductivity but quite different values. Overall, the method of Cooper et al. produces higher conductivity values in high permeability zones but lower values in low permeability areas than the Hvorslev method. Variances of the natural log of conductivity values derived from Hvorslev's and Bouwer and Rice's methods agree with those in the other aquifers under similar depositional environments. However, the variance calculated for the data based on the method of Cooper et al. appears unreasonably large. Despite these differences, histograms of the three sets of conductivity values exhibit bimodal distributions, reflecting stratification of the aquifer. Geostatistical analyses show that correlation lengths and statistical anisotropy of the hydraulic conductivity spatial structure varies with depth.

Combinatorics of geometrically distributed random variables: Left-to-right maxima

Assume that the numbers x 1, …, x n are the output of n independent geometrically distributed random variables. The number x i is a left-to-right maximum if it is greater (or equal, for a variation) than x 1, …, x i−1 . A precise average case analysis is performed for the parameter ‘number of left-to-right maxima’. The methods include generating functions and a technique from complex analysis, called Rice's method. Some additional results are also given.

A Note on Alternating Sums

We present some results on a certain type of alternating sums which frequently arise in connection with the average-case analysis of algorithms and data. Whereas the so-called Rice's method for treating such sums uses complex contour integration we perform manipulations of generating functions in order to get explicit results from which asymptotic estimates follow immediately.

Transformations to Reduce Boundary Bias in Kernel Density Estimation

SUMMARY We consider kernel estimation of a univariate density whose support is a compact interval. If the density is non-zero at either boundary, then the usual kernel estimator can be seriously biased. ‘Reflection’ at a boundary removes some bias, but unless the first derivative of the density is 0 at the boundary the estimator with reflection can still be much more severely biased at the boundary than in the interior. We propose to transform the data to a density that has its first derivative equal to 0 at both boundaries. The density of the transformed data is estimated, and an estimate of the density of the original data is obtained by a change of variables. The transformation is selected from a parametric family, which is allowed to be quite general in our theoretical study. We propose algorithms where the transformation is either a quartic polynomial, a β cumulative density function (CDF) or a linear combination of a polynomial and a β CDF. The last two types of transformation are designed to accommodate possible poles at the boundaries. The first two algorithms are tested on simulated data and compared with an adjusted kernel method of Rice. We find that our proposal performs similarly to Rice's for densities with one-sided derivatives at the boundaries. Unlike Rice's method, our proposal is guaranteed to produce non-negative estimates. This can be a distinct advantage when the density is 0 at either boundary. Our algorithm for densities with poles outperforms the Rice adjustment when the density has a pole at a boundary.

Fracture studies on a polyacetal—new thermoplastic polyurethane blend

AbstractStudies based on fracture mechanics have been made on polyacetal toughened with a synthesized thermoplastic polyurethane. The effects of elongation rate and defects like holes and notches on tensile properties have been investigated. Using three‐point bending specimens, fracture mechanics parameters such as strain energy release rate, G, Rice's contour integral, J, and fracture toughness, K have also been determined under plain stress conditions. The mechanical loss from the hysteresis curves, and ductile, brittle fractography using scanning electron microscopy have also been studied.