相关论文: St. Petersburg paradox and failure probability
Inspired by reliability issues in electric transmission networks, we use a probabilistic approach to study the occurrence of large failures in a stylized cascading failure model. In this model, lines have random capacities that initially…
Flutter instability in elastic structures subject to follower load, the most important cases being the famous Beck's and Pfluger's columns (two elastic rods in a cantilever configuration, with an additional concentrated mass at the end of…
Numerous field experiments suggest that the self-potential (SP) geophysical method may allow for the detection of hydraulically active fractures and provide information about fracture properties. However, a lack of suitable numerical tools…
If we assume that earthquakes are chaotic, and influenced locally then chaos theory suggests that there should be a temporal association between earthquakes in a local region that should be revealed with statistical examination. To date no…
In statistical mechanics, the generally called Stirling approximation is actually an approximation of Stirling's formula. In this article, it is shown that the term that is dropped is in fact the one that takes fluctuations into account.…
We show that G\"odel's negative results concerning arithmetic, which date back to the 1930s, and the ancient "sand pile" paradox (known also as "sorites paradox") pose the questions of the use of fuzzy sets and of the effect of a measuring…
Fluctuation theorems specify the non-zero probability to observe negative entropy production, contrary to a naive expectation from the second law of thermodynamics. For closed particle trajectories in a fluid, Stokes theorem can be used to…
Reasoning about causes and effects naturally arises in the engineering of safety-critical systems. A classical example is Fault Tree Analysis, a deductive technique used for system safety assessment, whereby an undesired state is reduced to…
Intermittency phenomena are known to be among the main reasons why Kolmogorov's theory of fully developed Turbulence is not in accordance with several experimental results. This is why some \emph{fractal} statistical models have been…
Numerical simulations of concrete fracture performed with a probabilistic mesoscale discrete model are presented. The model represents a substantial part of material randomness by assigning random locations to the largest aggregates. The…
We review statistical theories and numerical methods employed to consider the sample size dependence of the failure strength distribution of disordered materials. We first overview the analytical predictions of extreme value statistics and…
Cascading failures in power systems propagate non-locally, making the control and mitigation of outages extremely hard. In this work, we use the emerging concept of the tree partition of transmission networks to provide an analytical…
The statistical properties of failure are studied in a fiber bundle model with thermal noise. We show that the macroscopic failure is produced by a thermal activation of microcracks. Most importantly the effective temperature of the system…
One of the biggest perceived challenges in building megastructures, such as the space elevator, is the unavailability of materials with sufficient tensile strength. The presumed necessity of very strong materials stems from a design…
Recently, the educational initiative TED-Ed has published a popular brain teaser coined the 'frog riddle', which illustrates non-intuitive implications of conditional probabilities. In its intended form, the frog riddle is a reformulation…
Dirichlet processes and their extensions have reached a great popularity in Bayesian nonparametric statistics. They have also been introduced for spatial and spatio-temporal data, as a tool to analyze and predict surfaces. A popular…
We study the failure properties of fiber bundles when continuous rupture goes on due to the application of external load on the bundles. We take the two extreme models: equal load sharing model (democratic fiber bundles) and local load…
We provide a framework to bound the probability that accumulated errors were never above a given threshold on hybrid systems. Such systems are used for example to model an aircraft or a nuclear power plant on one side and its software on…
Two-sample network hypothesis testing is an important inference task with applications across diverse fields such as medicine, neuroscience, and sociology. Many of these testing methodologies operate under the implicit assumption that the…
Understanding failure in nanomaterials is critical for the design of reliable structural materials and small-scale devices that have components or microstructural elements at the nanometer length scale. No consensus exists on the effect of…