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1. Statistical Scaling in Localization-Induced Failures

   https://doi.org/10.1115/1.4065668  

   Le, Jia-Liang (November 2024, Applied Mechanics Reviews)

   Abstract The investigation of statistical scaling in localization-induced failures dates back to da Vinci's speculation on the length effect on rope strength in 1500 s. The early mathematical description of statistical scaling emerged with the birth of the extreme value statistics. The most commonly known mathematical model for statistical scaling is the Weibull size effect, which is a direct consequence of the infinite weakest-link model. However, abundant experimental observations on various localization-induced failures have shown that the Weibull size effect is inadequate. Over the last two decades, two mathematical models were developed to describe the statistical size effect in localization-induced failures. One is the finite weakest-link model, in which the random structural resistance is expressed as the minimum of a set of independent discrete random variables. The other is the level excursion model, a continuum description of the finite weakest-link model, in which the structural failure probability is calculated as the probability of the upcrossing of a random field over a barrier. This paper reviews the mathematical formulation of these two models and their applications to various engineering problems including the strength distributions of quasi-brittle structures, failure statistics of micro-electromechanical systems (MEMS) devices, breakdown statistics of high– k gate dielectrics, and probability distribution of buckling pressure of spherical shells containing random geometric imperfections. In addition, the implications of statistical scaling for the stochastic finite element simulations and the reliability-based structural design are discussed. In particular, the recent development of the size-dependent safety factors is reviewed. 

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2. Modeling of rock inhomogeneity and anisotropy by explicit and implicit representation of microcracks

   Abedi, R.; Clarke, P.L. (January 2018, Proceeding 52th U.S. Rock Mechanics/Geomechanics Symposium)

   Fracture patterns experienced under a dynamic uniaxial compressive load are highly sensitive to rock microstructural defects due to its brittleness and the absence of macroscopic stress concentration points. We propose two different approaches for modeling rock microstructural defects and inhomogeneity. In the explicit realization approach, microcracks with certain statistics are incorporated in the computational domain. In the implicit realization approach, fracture strength values are sampled using a Weibull probability distribution. We use the Mohr-Coulomb failure criterion to define an effective stress in the context of an interfacial damage model. This model predicts crack propagation at angles ±ɸch = ±(45 − ɸ/2) relative to the direction of compressive load, where ɸ is the friction angle. By using appropriate models for fracture strength anisotropy, we demonstrate the interaction of rock weakest plane and ɸch. Numerical results demonstrate the greater effect of strength anisotropy on fracture pattern when an explicit approach is employed. In addition, the density of fractures increases as the angle of the weakest planes approaches ±ɸch. The fracture simulations are performed by an h-adaptive asynchronous spacetime discontinuous Galerkin (aSDG) method that can accommodate crack propagation in any directions. 

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3. Confident Monte Carlo: Rigorous Analysis of Guessing Curves for Probabilistic Password Models

   https://doi.org/10.1109/SP46215.2023.10179365  

   Liu, Peiyuan; Blocki, Jeremiah; Bai, Wenjie (May 2023, IEEE)

   In password security a defender would like to identify and warn users with weak passwords. Similarly, the defender may also want to predict what fraction of passwords would be cracked within B guesses as the attacker’s guessing budget B varies from small (online attacker) to large (offline attacker). Towards each of these goals the defender would like to quickly estimate the guessing number for each user password pwd assuming that the attacker uses a password cracking model M i.e., how many password guesses will the attacker check before s/he cracks each user password pwd. Since naïve brute-force enumeration can be prohibitively expensive when the guessing number is very large, Dell’Amico and Filippone [1] developed an efficient Monte Carlo algorithm to estimate the guessing number of a given password pwd. While Dell’Amico and Filippone proved that their estimator is unbiased there is no guarantee that the Monte Carlo estimates are accurate nor does the method provide confidence ranges on the estimated guessing number or even indicate if/when there is a higher degree of uncertainty.Our contributions are as follows: First, we identify theoretical examples where, with high probability, Monte Carlo Strength estimation produces highly inaccurate estimates of individual guessing numbers as well as the entire guessing curve. Second, we introduce Confident Monte Carlo Strength Estimation as an extension of Dell’Amico and Filippone [1]. Given a password our estimator generates an upper and lower bound with the guarantee that, except with probability δ, the true guessing number lies within the given confidence range. Our techniques can also be used to characterize the attacker’s guessing curve. In particular, given a probabilistic password cracking model M we can generate high confidence upper and lower bounds on the fraction of passwords that the attacker will crack as the guessing budget B varies. 

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4. Quantifying the Interdependency Strength Across Critical Infrastructure Systems Using A Dynamic Network Flow Redistribution Model.

   Wang, Y.; Yu, J.; Baroud, H. (July 2020, Proceedings of the 30th European Safety and Reliability Conference and 15th Probabilistic Safety Assessment and Management Conference.)

   Baraldi, P.; null; Zio, E. (Ed.)

   Critical infrastructure networks are becoming increasingly interdependent which adversely impacts their performance through the cascading effect of initial failures. Failing to account for these complex interactions could lead to an underestimation of the vulnerability of interdependent critical infrastructure (ICI). The goal of this research is to assess how important interdependent links are by evaluating the interdependency strength using a dynamic network flow redistribution model which accounts for the dynamic and uncertain aspects of interdependencies. Specifically, a vulnerability analysis is performed considering two scenarios, one with interdependent links and the other without interdependent links. The initial failure is set to be the same under both scenarios. Cascading failure is modeled through a flow redistribution until the entire system reaches a stable state in which cascading failure no longer occurs. The unmet demand of the networks at the stable state over the initial demand is defined as the vulnerability. The difference between the vulnerability of each network under these two scenarios is used as the metric to quantify interdependency strength. A case study of a real power-water-gas system subject to earthquake risk is conducted to illustrate the proposed method. Uncertainty is incorporated by considering failure probability using Monte Carlo simulation. By varying the location and magnitude of earthquake disruptions, we show that interdependency strength is determined not only by the topology and flow of ICIs but also the characteristics of the disruptions. This compound system-disruption effect on interdependency strength can inform the design, assessment, and restoration of ICIs. 

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5. Nonequilibrium steady-state dynamics of Markov processes on graphs

   https://doi.org/10.21468/SciPostPhys.19.2.045  

   Crotti, Stefano; Barthel, Thomas; Braunstein, Alfredo (August 2025, SciPost Physics)

   We propose an analytic approach for the steady-state dynamics of Markov processes on locally tree-like graphs. It is based on time-translation invariant probability distributions for edge trajectories, which we encode in terms of infinite matrix products. For homogeneous ensembles on regular graphs, the distribution is parametrized by a single d×d×r^2 tensor, where r is the number of states per variable, and d is the matrix-product bond dimension. While the method becomes exact in the large-d limit, it typically provides highly accurate results even for small bond dimensions d. The d^2r^2 parameters are determined by solving a fixed point equation, for which we provide an efficient belief-propagation procedure. We apply this approach to a variety of models, including Ising-Glauber dynamics with symmetric and asymmetric couplings, as well as the SIS model. Even for small d, the results are compatible with Monte Carlo estimates and accurately reproduce known exact solutions. The method provides access to precise temporal correlations, which, in some regimes, would be virtually impossible to estimate by sampling. 

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