Frequency-magnitude statistics for natural hazards can greatly help in probabilistic hazard assessments. An example is the case of earthquakes, where the generality of a power-law (fractal) frequency-rupture area correlation is a major feature in seismic risk mapping. Other examples of this power-law frequency-size behaviour are landslides and wildfires. In previous studies, authors have made t...

In this article, we consider Zipf-Mandelbrot law as applied to texts in natural languages. We present a simple model of dependence of the law on the text size, which is featured by variable power-law tail and constant ratio of the most frequent words. As a result we derive several closed formulas, which accord with empirical data qualitatively and partially quantitatively. For example, there ap...

Populations vary in time and in space, and temporal variation may differ from spatial variation. Yet, in the past half century, field data have confirmed both the temporal and spatial forms of Taylor's power Law, a linear relationship between log(variance) and log(mean) of population size. Recent theory predicted that competitive species interactions should reduce the slope of the temporal vers...

n-tuple power law widely exists in language, computer program code, DNA and music. After a vast amount of Zipf analyses of n-tuple power law from empirical data, we propose a model to explain the n-tuple power law feature existed in these information translational carriers. Our model is a preferential selection approach inspired by Simon’s model which explained scaling law of single symbol in a...

A simple analytical model to predict the DC MOSFET behavior under electromagnetic interference (EMI) is presented. The model is able to describe the MOSFET performance in the linear and saturation regions under EMI disturbance applied to the gate. The model consists of a unique simple equivalent circuit based on a voltage dependent current source and a reduced number of parameters which can acc...

Nanoflares have been proposed as the main source of heating of the solar corona. However, detecting them directly has so far proved elusive, and extrapolating to them from the properties of larger brightenings gives unreliable estimates of the power-law exponent α characterising their distribution. Here we take the approach of statistically modelling light curves representative of the quiet Sun...

The benefits from practice follow a nonlinear function: Improvement is rapid at first but decreases as the practitioner becomes more skilled (see, e.g., Thorndike, 1913). The idea that a simple nonlinear function might describe practice effects in a broad range of tasks was championed by Newell and Rosenbloom’s (1981) influential chapter entitled “Mechanisms of Skill Acquisition and the Law of ...

In the present work, study of the vibration of a functionally graded (FG) cylindrical shell made up of stainless steel, zirconia, and nickel is presented. Free vibration analysis is presented for FG cylindrical shells with simply supported-simply supported and clamped–clamped boundary condition based on temperature independent material properties. The equations of motion are derived by Hamilton...