Extreme event statistics of daily rainfall: Dynamical systems approach

We analyse the probability densities of daily rainfall amounts at a variety of locations on the Earth. The observed distributions of the amount of rainfall fit well to a q-exponential distribution with exponent q close to q=1.3. We discuss possible reasons for the emergence of this power law. On the contrary, the waiting time distribution between rainy days is observed to follow a near-exponential distribution. A careful investigation shows that a q-exponential with q=1.05 yields actually the best fit of the data. A Poisson process where the rate fluctuates slightly in a superstatistical way is discussed as a possible model for this. We discuss the extreme value statistics for extreme daily rainfall, which can potentially lead to flooding. This is described by Frechet distributions as the corresponding distributions of the amount of daily rainfall decay with a power law. On the other hand, looking at extreme event statistics of waiting times between rainy days (leading to droughts for very long dry periods) we obtain from the observed near-exponential decay of waiting times an extreme event statistics close to Gumbel distributions. We discuss superstatistical dynamical systems as simple models in this context.Comment: 10 pages, 15 figures. Replaced by final version published in J.Phys.

Extreme Value Laws for Superstatistics

We study the extreme value distribution of stochastic processes modeled by superstatistics. Classical extreme value theory asserts that (under mild asymptotic independence assumptions) only three possible limit distributions are possible, namely: Gumbel, Fr\'echet and Weibull distribution. On the other hand, superstatistics contains three important universality classes, namely $\chi^2$-superstatistics, inverse $\chi^2$-superstatistics, and lognormal superstatistics, all maximizing different effective entropy measures. We investigate how the three classes of extreme value theory are related to the three classes of superstatistics. We show that for any superstatistical process whose local equilibrium distribution does not live on a finite support, the Weibull distribution cannot occur. Under the above mild asymptotic independence assumptions, we also show that $\chi^2$-superstatistics generally leads an extreme value statistics described by a Fr\'echet distribution, whereas inverse $\chi^2$-superstatistics, as well as lognormal superstatistics, lead to an extreme value statistics associated with the Gumbel distribution.Comment: To appear in Entrop

Using imprecise continuous time Markov chains for assessing the reliability of power networks with common cause failure and non-immediate repair.

We explore how imprecise continuous time Markov chains can improve traditional reliability models based on precise continuous time Markov chains. Specifically, we analyse the reliability of power networks under very weak statistical assumptions, explicitly accounting for non-stationary failure and repair rates and the limited accuracy by which common cause failure rates can be estimated. Bounds on typical quantities of interest are derived, namely the expected time spent in system failure state, as well as the expected number of transitions to that state. A worked numerical example demonstrates the theoretical techniques described. Interestingly, the number of iterations required for convergence is observed to be much lower than current theoretical bounds

High-performance Parallel Solver for Integral Equations of Electromagnetics Based on Galerkin Method

A new parallel solver for the volumetric integral equations (IE) of electrodynamics is presented. The solver is based on the Galerkin method which ensures the convergent numerical solution. The main features include: (i) the memory usage is 8 times lower, compared to analogous IE based algorithms, without additional restriction on the background media; (ii) accurate and stable method to compute matrix coefficients corresponding to the IE; (iii) high degree of parallelism. The solver's computational efficiency is shown on a problem of magnetotelluric sounding of the high conductivity contrast media. A good agreement with the results obtained with the second order finite element method is demonstrated. Due to effective approach to parallelization and distributed data storage the program exhibits perfect scalability on different hardware platforms.Comment: The main results of this paper were presented at IAMG 2015 conference Frieberg, Germany. 28 pages, 11 figure