Approximate Solutions of the Space-Fractional Diffusion Equations with Additive Noise

In this article we take into account a class of stochastic space diffusion equations with polynomials forced by additive noise. We derive rigorously limiting equations which de…ne the critical dynamics. Also, we approximate solutions of stochastic fractional space di¤usion equations with polynomial term by limiting equations, which are ordinary di¤er-ential equations. Moreover, we address the e¤ect of the noise on the solution’s stabilization. Finally, we apply our results to Fisher’s equation and Ginzburg–Landau models.

Predicting Morphodynamics for Beach Intertidal Systems in the North Sea: A Space-Time Stochastic Approach

The ability to accurately predict beach morphodynamics is of primary interest for coastal scientists and managers. With this goal in mind, a stochastic model of a sandy macrotidal barred beach is developed that is based on cross-shore elevation profiles. Intertidal elevation was monitored from monthly to annually for 19 years through Real Time Kinematics-GPS (RTK-GPS) and LiDAR surveys, and monthly during two years with an RTK-GPS. In addition, during two campaigns of about two weeks, intensive surveys on a daily basis were performed with an RTK-GPS on a different set of profiles. Based on the measurements, space and time variograms are constructed in order to assess the spatial and temporal dependencies of these elevations. A separable space-time covariance model is then built from them in order to generate a large number of plausible future profiles at arbitrary time instants t+τ, starting from observed profiles at time instants t. For each simulation, the total displaced sand volume is computed and a distribution is obtained. The mean of this distribution is in good agreement with the total displaced sand volume measured on the profiles, provided that they are lower than 45 m3/m. The time variogram also shows that 90% of maximum variability is reached for a time interval τ of three years. These results demonstrate how the temporal evolution of an integrated property, like the total displaced sand volume, can be estimated over time. This suggests that a similar stochastic approach could be useful for estimating other properties as long as one is able to capture the stochastic space-time variability of the underlying processes.

Divide and Compact — Stochastic Space Compaction for Faster-than-at-Speed Test

With shrinking feature sizes detecting small delay faults is getting more and more important. But not all small delay faults are detectable during at-speed test. By overclocking the circuit with several different test frequencies faster-than-at-speed test (FAST) is able to detect these hidden delay faults. If the clock frequency is increased, some outputs of the circuit may not have stabilized yet, and these outputs have to be considered as unknown ([Formula: see text]-values). These [Formula: see text]-values impede the test response compaction. In addition, the number and distribution of the [Formula: see text]-values vary with the clock frequency, and thus a very flexible [Formula: see text]-handling is needed for FAST. Most of the state-of-the-art solutions are not designed for these varying [Formula: see text]-profiles. Yet, the stochastic compactor by Mitra et al. can be adjusted to changing environments. It is easily programmable because it is controlled by weighted pseudo-random signals. But an optimal setup cannot be guaranteed in a FAST scenario. By partitioning the compactor into several smaller ones and a proper mapping of the scan outputs to the compactor inputs, the compactor can be better adapted to the varying [Formula: see text]-profiles. Finding the best setup can be formulated as a set partitioning problem. To solve this problem, several algorithms are presented. Experimental results show that independent from the scan chain configuration, the number of [Formula: see text]-values can be reduced significantly while the fault efficiency can be maintained. Additionally, it is shown that [Formula: see text]-reduction and fault efficiency can be adapted to user-defined goals.

Stochastic Galerkin method for cloud simulation

We develop a stochastic Galerkin method for a coupled Navier-Stokes-cloud system that models dynamics of warm clouds. Our goal is to explicitly describe the evolution of uncertainties that arise due to unknown input data, such as model parameters and initial or boundary conditions. The developed stochastic Galerkin method combines the space-time approximation obtained by a suitable finite volume method with a spectral-type approximation based on the generalized polynomial chaos expansion in the stochastic space. The resulting numerical scheme yields a second-order accurate approximation in both space and time and exponential convergence in the stochastic space. Our numerical results demonstrate the reliability and robustness of the stochastic Galerkin method. We also use the proposed method to study the behavior of clouds in certain perturbed scenarios, for examples, the ones leading to changes in macroscopic cloud pattern as a shift from hexagonal to rectangular structures.

Pysteps: an open-source Python library for probabilistic precipitation nowcasting (v1.0)

Pysteps is an open-source and community-driven Python library for probabilistic precipitation nowcasting, that is, very-short-range forecasting (0–6 h). The aim of pysteps is to serve two different needs. The first is to provide a modular and well-documented framework for researchers interested in developing new methods for nowcasting and stochastic space–time simulation of precipitation. The second aim is to offer a highly configurable and easily accessible platform for practitioners ranging from weather forecasters to hydrologists. In this sense, pysteps has the potential to become an important component for integrated early warning systems for severe weather. The pysteps library supports various input/output file formats and implements several optical flow methods as well as advanced stochastic generators to produce ensemble nowcasts. In addition, it includes tools for visualizing and post-processing the nowcasts and methods for deterministic, probabilistic and neighborhood forecast verification. The pysteps library is described and its potential is demonstrated using radar composite images from Finland, Switzerland, the United States and Australia. Finally, scientific experiments are carried out to help the reader to understand the pysteps framework and sensitivity to model parameters.