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A theoretical method to determine the initial fracture toughness K I ini of concrete for central-notched split-tension specimens was developed based on the extreme theory. In this method, the K I ini , critical crack tip opening displacement CTOD c , and half critical effective crack extension Δ ɑ c could be obtained by the experimental peak load of a single specimen. The measurement of critical crack mouth opening displacement CMOD c was unnecessary in this method. The fracture parameters were calculated using the cube and cylinder split-tension specimens. Results showed that the values of K I ini obtained by the proposed method were slightly smaller than those obtained by the double- K method, and the difference between them generally decreases with the loading rates. And the values of CTOD c and Δ ɑ c obtained by the proposed method were more stable compared with those obtained by the double- K method. [ABSTRACT FROM AUTHOR]

Completing the study initiated by Mounaix and Collet (J Stat Phys 143:139-147, ), we investigate the realizations of a Gaussian random field in the limit where a given (general) quadratic form of the field is large. Concentration in $$L^2$$ and in probability is proved under mild conditions and the resulting quasi-deterministic behavior of the field is given. Applications to a large local quadratic form are considered in two specific cases. In particular, the quasi-deterministic structure of a Gaussian random flow with a large local helicity at some given point is determined explicitly. [ABSTRACT FROM AUTHOR]

• Size effect on the unstable fracture toughness of quartz-diorite rock is investigated based on the analytical method. • Unstable fracture toughness of rock specimen increases with the increase of specimen depth. • Unstable fracture toughness will converge to the size-independent fracture toughness of Bažant's size effect model. • Unstable fracture toughness changes with the alteration of initial normalized crack length. • Specimen depth and boundary affect the rock unstable fracture toughness. In this paper, an analytical method was introduced to investigate the size effect on the unstable fracture toughness of fine-grained quartz-diorite. The analytical method can predict the axial load, crack mouth opening displacement, and crack resistance curve of the three-point bend specimen when the elastic modulus, tensile strength, fracture energy, and initial fracture toughness are given. Mode I fracture tests were conducted on the three-point bend specimen with five different depths to acquire these parameters. And, the effectiveness of the analytical method was validated by the experimental results. The analytical method is then utilized to compute the unstable fracture toughness of three-point bend specimens with different sizes and normalized initial crack lengths. The results reveal that unstable fracture toughness is a size-dependent parameter that first increases and then remains unchanged with the increase of the specimen size. The nominal stress follows Bažant's size effect law and the unstable fracture toughness will converge to the size-independent mode I fracture toughness obtained by Bažant's size effect model with the increase of specimen depth. Furthermore, for the specimen with a small depth, unstable fracture toughness decreases with the increase in normalized initial crack length, which further illustrates the boundary effect on the unstable fracture toughness of rock specimens. [ABSTRACT FROM AUTHOR]

In the context of linear amplification for systems driven by the square of a Gaussian noise, we investigate the realizations of a Gaussian field in the limit where its L-norm is large. Concentration onto the eigenspace associated with the largest eigenvalue of the covariance of the field is proved. When the covariance is trace class, the concentration is in probability for the L-norm. A stronger concentration, in mean for the sup-norm, is proved for a smaller class of Gaussian fields, and an example of a field belonging to that class is given. A possible connection with Bose-Einstein condensation is briefly discussed. [ABSTRACT FROM AUTHOR]

Extremal properties of the statistics of speckle pattern are studied in the context of so-called “optically smoothed” light beams of laser-matter interaction. It is shown that the asymptotic statistics of the highest intensity in a speckle pattern, which can be associated with the most intense speckles, follows a Gumbel law, which is in agreement with numerical simulations. It is found that the probability density function of the most intense speckle peaks around the value corresponding to the logarithm of the number of speckles in the considered volume times the average intensity value of the speckle pattern. This result is of great interest for nonlinear processes, like instabilities, where extreme speckles play an important role. [ABSTRACT FROM AUTHOR]

Abstract: The concentrations of air pollutants depend on meteorological conditions and pollutant emission level. From the statistical properties of air pollutants the number of times the daily average concentrations exceed the assigned air quality standard (AQS) can be estimated, as well as the level of reduction of particle matter emission sources required to meet the AQS. In this paper three statistical distributions (lognormal, Weibull and type V Pearson distribution) were used to fit the complete set of PM10 data for the Belgrade urban area during a three-year period (2003–2005). The method of moments and the method of least squares were both used to estimate the parameters of the three theoretical distributions. The type V Pearson distribution represented the PM10 daily average concentration most closely. However, the parent distributions sometimes diverged in predicting a high PM10 concentration and therefore asymptotic distributions of extreme values were used to fit the high PM10 concentration distribution more correctly. This method can successfully predict the return period and exceedances over a critical concentration in succeeding years. The estimated emission source reduction of PM10 to meet the assigned standard varied from 53% to 63% in the Belgrade urban area. The results provide useful information for air quality management and could be used to examine the similarities and differences among air pollution types in diverse areas. [Copyright &y& Elsevier]

Abstract: We prove almost sure limit theorems for the maximum of a stationary normal sequence under some conditions. [Copyright &y& Elsevier]