Simulations and Experiments of Stochastic Characteristics for Collective Short Fatigue Cracks in Steels

Stochastic characteristics prevail in the process of short fatigue crack progression. This paper presents a method taking into account the balance of crack number density to describe the stochastic behaviour of short crack collective evolution. The results from the simulation illustrate the stochastic development of short cracks. The experiments on two types of steels show the random distribution for collective short cracks with the number of cracks and the maximum crack length as a function of different locations on specimen surface. The experiments also give the variation of total number of short cracks with fatigue cycles. The test results are consistent with numerical simulations.

Stochastic Structural Model of Rock and Soil Aggregates by Continuum-Based Discrete Element Method

This paper first presents a stochastic structural model to describe the random geometrical features of rock and soil aggregates. The stochastic structural model uses mixture ratio, rock size and rock shape to construct the microstructures of aggregates,and introduces two types of structural elements (block element and jointed element) and three types of material elements (rock element, soil element, and weaker jointed element)for this microstructure. Then, continuum-based discrete element method is used to study the deformation and failure mechanism of rock and soil aggregate through a series of loading tests. It is found that the stress-strain curve of rock and soil aggregates is nonlinear, and the failure is usually initialized from weaker jointed elements. Finally, some factors such as mixture ratio, rock size and rock shape are studied in detail. The numerical results are in good agreement with in situ test. Therefore, current model is effective for simulating the mechanical behaviors of rock and soil aggregates.

Influence of stochastic mesoscopic structure on macroscopic mechanical behavior of brittle material

A newly developed numerical code, MFPA(2D) (Material Failure Process Analysis), is applied to study the influence of stochastic mesoscopic structure on macroscopic mechanical behavior of rock-like materials. A set of uniaxial compression tests has been numerically studied with numerical specimens containing pre-existing crack-like flaw. The numerical results reveal the influence of random mesoscopic structure on failure process of brittle material, which indicates that the variation of failure mode is strongly sensitive to the local disorder feature of the specimen. And the patterns of the crack evolution in the specimens are very different from each other due to the random mesoscopic structure in material. The results give a good explanation for various kinds of fracture modes and peak strength variation observed in laboratory studies with specimens made from the same rock block being statistically homogenous in macro scale. In addition, the evolution of crack is more complicated in heterogeneous cases than in homogeneous cases.

Statistical and stochastic description of microvoid evolution observed in dynamic failure of ductile materials

A brief review is presented of statistical approaches on microdamage evolution. An experimental study of statistical microdamage evolution in two ductile materials under dynamic loading is carried out. The observation indicates that there are large differences in size and distribution of microvoids between these two materials. With this phenomenon in mind, kinetic equations governing the nucleation and growth of microvoids in nonlinear rate-dependent materials are combined with the balance law of void number to establish statistical differential equations that describe the evolution of microvoids' number density. The theoretical solution provides a reasonable explanation of the experimentally observed phenomenon. The effects of stochastic fluctuation which is influenced by the inhomogeneous microscopic structure of materials are subsequently examined (i.e. stochastic growth model). Based on the stochastic differential equation, a Fokker-Planck equation which governs the evolution of the transition probability is derived. The analytical solution for the transition probability is then obtained and the effects of stochastic fluctuation is discussed. The statistical and stochastic analyses may provide effective approaches to reveal the physics of damage evolution and dynamic failure process in ductile materials.

A theoretical analysis on stochastic behaviour of short cracks and fatigue damage of metals

In this paper, the closed form of solution to the stochastic differential equation for a fatigue crack evolution system is derived. and the relationship between metal fatigue damage and crack stochastic behaviour is investigated. It is found that the damage extent of metals is independent of crack stochastic behaviour ii the stochastic deviation of the crack growth rate is directly proportional to its mean value. The evolution of stochastic deviation of metal fatigue damage in the stage close to the transition point between short and long crack regimes is also discussed.

A stochastic jump and deterministic dynamics model of impact failure evolution with rate effect

Motivated by the observation of the rate effect on material failure, a model of nonlinear and nonlocal evolution is developed, that includes both stochastic and dynamic effects. In phase space a transitional region prevails, which distinguishes the failure behavior from a globally stable one to that of catastrophic. Several probability functions are found to characterize the distinctive features of evolution due to different degrees of nucleation, growth and coalescence rates. The results may provide a better understanding of material failure.

Local exponential divergence plot and optimal embedding of a chaotic time-series

we propose here a local exponential divergence plot which is capable of providing a new means of characterizing chaotic time series. The suggested plot defines a time dependent exponent LAMBDA and a ''plus'' exponent LAMBDA+ which serves as a criterion for estimating simultaneously the minimal acceptable embedding dimension, the proper delay time and the largest Lyapunov exponent.

A perturbational h4 exponential finite-difference scheme for the convective diffusion equation

A perturbational h4 compact exponential finite difference scheme with diagonally dominant coefficient matrix and upwind effect is developed for the convective diffusion equation. Perturbations of second order are exerted on the convective coefficients and source term of an h2 exponential finite difference scheme proposed in this paper based on a transformation to eliminate the upwind effect of the convective diffusion equation. Four numerical examples including one- to three-dimensional model equations of fluid flow and a problem of natural convective heat transfer are given to illustrate the excellent behavior of the present exponential schemes, the h4 accuracy of the perturbational scheme is verified using double precision arithmetic.

H4 exponential finite-difference scheme for convective diffusion-equations

Perturbations are applied to the convective coefficients and source term of a convection-diffusion equation so that second-order corrections may be applied to a second-order exponential scheme. The basic Structure of the equations in the resulting fourth-order scheme is identical to that for the second order. Furthermore, the calculations are quite simple as the second-order corrections may be obtained in a single pass using a second-order scheme. For one to three dimensions, the fourth-order exponential scheme is unconditionally stable. As examples, the method is applied to Burgers' and other fluid mechanics problems. Compared with schemes normally used, the accuracies are found to be good and the method is applicable to regions with large gradients.

Effects of stochastic extension in ideal microcrack system

The effects of stochastic extension on the statistical evolution of the ideal microcrack system are discussed. First, a general theoretical formulation and an expression for the transition probability of extension process are presented, then the features of evolution in stochastic model are demonstrated by several numerical results and compared with that in deterministic model.

Anisotropic-source-induced changes of the degree of polarization of stochastic electromagnetic beams on propagation

It is shown that stochastic electromagnetic beams may have different degrees of polarization on propagation, even though they have the same coherence properties in the source plane. This fact is due to a possible difference in the anisotropy of the field in the source plane. The result is illustrated by some examples.

Exploring consensus mRNA secondary (folding) structure units by stochastic sampling and folding simulation

It is extremely difficult to explore mRNA folding structure by biological experiments. In this report, we use stochastic sampling and folding simulation to test the existence of the stable secondary structural units of-mRNA, look for the folding units, and explore the probabilistic stabilization of the units. Using this method, We made simulations for all possible local optimum secondary structures of a single strand mRNA within a certain range, and searched for the common parts of the secondary structures. The consensus secondary structure units (CSSUs) extracted from the above method are mainly hairpins, with a few single strands. These CSSUs suggest that the mRNA folding units could be relatively stable and could perform specific biological function. The significance of these observations for the mRNA folding problem in general is also discussed. (c) 2004 Elsevier B.V. All rights reserved.

Stochastic resonance for modulated gain in a single-mode laser

Stochastic resonance (SR) induced by the signal modulation is investigated, by introducing the signal-modulated gain into a single-mode laser system. Using the linear approximation method, we detailedly calculate the signal-to-noise ratio (SNR) of a gain-noise model of the single-mode laser, taking the cross-correlation between the quantum noise and pump noise into account. We find that, SR appears in the dependence of the SNR on the intensities of the quantum and the pump noises when the correlation coefficient between both the noises is negative; moreover, when the cross-correlation between the two noises is strongly negative, SR exhibits a resonance and a suppression versus the gain coefficient, meanwhile, the single-peaked SR and multi-peaked SR occur in the behaviors of the SNR as functions of the loss coefficient and the deterministic steady-state intensity. (c) 2005 Elsevier B.V. All rights reserved.

Non-exponential photoluminescence decay dynamics of localized carriers in disordered InGaN/GaN quantum wells: the role of localization length

In this article, we report a combined experimental and theoretical study on the luminescence dynamics of localized carriers in disordered InGaN/GaN quantum wells. The luminescence intensity of localized carriers is found to exhibit an unusual non-exponential decay. Adopting a new model taking the radiative recombination and phonon-assisted hopping transition between different localized states into account, which was recently developed by Rubel et al., the non-exponential decay behavior of the carriers can be quantitatively interpreted. Combining with precise structure characterization, the theoretical simulations show that the localization length of localized carriers is a key parameter governing their luminescence decay dynamics. (c) 2006 Optical Society of America.

Stochastic resonance in single-mode semiconductor lasers

Owing to the considerable virtues of semiconductor lasers for applications, they have become the main optical source for fiber communication systems recently. The behavior of stochastic resonance (SR) in direct-modulated semiconductor laser systems is investigated in this article. Considering the carrier and photon noises and the cross-correlation between the two noises, the power spectrum of the photon density and the signal-to-noise ratio (SNR) of the modulated laser system were calculated using the linear approximation method. We found that the SR always appears in the dependence of the SNR upon the bias current density, and is strongly affected by the cross-correlation coefficient of the carrier and photon noises, the frequency of modulation signal and the photon lifetime in the laser cavity. Hence, it is promising to use the SR mechanism to enhance the SNR of direct-modulated semiconductor laser systems and improve the quality of optical communication. (c) 2006 Elsevier B.V. All rights reserved.