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تسجيل مستخدم جديدFiber Bundle model with Highly Disordered Breaking Thresholds
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We present a study of the fiber bundle model using equal load sharing dynamics where the breaking thresholds of the fibers are drawn randomly from a power law distribution of the form $p(b)sim b^{-1}$ in the range $10^{-beta}$ to $10^{beta}$. Tuning the value of $beta$ continuously over a wide range, the critical behavior of the fiber bundle has been studied both analytically as well as numerically. Our results are: (i) The critical load $sigma_c(beta,N)$ for the bundle of size $N$ approaches its asymptotic value $sigma_c(beta)$ as $sigma_c(beta,N) = sigma_c(beta)+AN^{-1/ u(beta)}$ where $sigma_c(beta)$ has been obtained analytically as $sigma_c(beta) = 10^beta/(2beta eln10)$ for $beta geq beta_u = 1/(2ln10)$, and for $beta<beta_u$ the weakest fiber failure leads to the catastrophic breakdown of the entire fiber bundle, similar to brittle materials, leading to $sigma_c(beta) = 10^{-beta}$; (ii) the fraction of broken fibers right before the complete breakdown of the bundle has the form $1-1/(2beta ln10)$; (iii) the distribution $D(Delta)$ of the avalanches of size $Delta$ follows a power law $D(Delta)sim Delta^{-xi}$ with $xi = 5/2$ for $Delta gg Delta_c(beta)$ and $xi = 3/2$ for $Delta ll Delta_c(beta)$, where the crossover avalanche size $Delta_c(beta) = 2/(1-e10^{-2beta})^2$.
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