Department of Earth Sciences, Utrecht University, Princetonlaan 8a, Utrecht 3594 CB, The Netherlands.
Published: March 2022
AI Article Synopsis
Article Abstract
In this paper, we consider a simplified model of turbulence for large Reynolds numbers driven by a constant power energy input on large scales. In the statistical stationary regime, the behaviour of the kinetic energy is characterized by two well-defined phases: a laminar phase where the kinetic energy grows linearly for a (random) time [Formula: see text] followed by abrupt avalanche-like energy drops of sizes [Formula: see text] due to strong intermittent fluctuations of energy dissipation. We study the probability distribution [Formula: see text] and [Formula: see text] which both exhibit a quite well-defined scaling behaviour. Although [Formula: see text] and [Formula: see text] are not statistically correlated, we suggest and numerically checked that their scaling properties are related based on a simple, but non-trivial, scaling argument. We propose that the same approach can be used for other systems showing avalanche-like behaviour such as amorphous solids and seismic events. This article is part of the theme issue 'Scaling the turbulence edifice (part 1)'.
We derive a compact expression for the second-order correlation function [Formula: see text] of a quantum state in terms of its Wigner function, thereby establishing a direct link between [Formula: see text] and the state's shape in phase space. We conduct an experiment that simultaneously measures [Formula: see text] through direct photocounting and reconstructs the Wigner function via homodyne tomography. The results confirm our theoretical predictions.
The rice plant is one of the most significant crops in the world, and it suffers from various diseases. The traditional methods for rice disease detection are complex and time-consuming, mainly depending on the expert's experience. The explosive growth in image processing, computer vision, and deep learning techniques provides effective and innovative agriculture solutions for automatically detecting and classifying these diseases.
This manuscript explores the stability theory of several stochastic/random models. It delves into analyzing the stability of equilibrium states in systems influenced by standard Brownian motion and exhibit random variable coefficients. By constructing appropriate Lyapunov functions, various types of stability are identified, each associated with distinct stability conditions.
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RMSProp is one of the most popular stochastic optimization algorithms in deep learning applications. However, recent work has pointed out that this method may not converge to the optimal solution even in simple convex settings. To this end, we propose a time-varying version of RMSProp to fix the non-convergence issues.
