Metal–Covalent Organic Frameworks (MCOFs): A Bridge Between Metal–Organic Frameworks and Covalent Organic Frameworks

Many sophisticated chemical and physical properties of porous materials strongly rely on the presence of the metal ions within the structures. Whereas homogeneous distribution of metals is conveniently realized in metal–organic frameworks (MOFs), the limited stability potentially restricts their practical implementation. From that perspective, the development of metal–covalent organic frameworks (MCOFs) may address these shortcomings by incorporating active metal species atop highly stable COF backbones. This Minireview highlights examples of MCOFs that tackle important issues from their design, synthesis, characterization to cutting‐edge applications.     

Random attractor for the Ladyzhenskaya model with additive noise

This paper studies the dynamical behavior of the Ladyzhenskaya model with additive noise. With some conditions, we prove that the generated random dynamical system has a compact random attractor, which is a random compact set absorbing any bounded nonrandom subset of the phase space.     

Synchronization of systems of Marcus canonical equations driven by α-stable noises

Dynamical systems driven by Gaussian noises have been considered extensively in modeling, simulation and theory. However, complex systems in engineering and science are often subject to non-Gaussian fluctuations or uncertainties. A coupled dynamical system under non-Gaussian Lévy noise is considered. After discussing cocycle property, stationary orbits and random attractors, a synchronization phenomenon is shown to occur, when the drift terms of the coupled system satisfy certain dissipativity conditions. The synchronization result implies that coupled dynamical systems share a dynamical feature in certain asymptotic sense.     

ELEMENTARY BIFURCATIONS FOR A SIMPLE DYNAMICAL SYSTEM UNDER NON-GAUSSIAN LEVY NOISES

Nonlinear dynamical systems are sometimes under the influence of random fluctuations. It is desirable to examine possible bifurcations for stochastic dynamical systems when a parameter varies. A computational analysis is conducted to investigate bifurcations of a simple dynamical system under non-Gaussian α-stable Lévy motions, by examining the changes in stationary probability density functions for the solution orbits of this stochastic system. The stationary probability density functions are obtained by solving a nonlocal Fokker-Planck equation numerically. This allows numerically investigating phenomenological bifurcation, or P-bifurcation, for stochastic differential equations with non-Gaussian Lévy noises.     

A machine learning method for computing quasi-potential of stochastic dynamical systems

Nonlinear Dynamics - The concept of quasi-potential plays a central role in understanding the mechanisms of rare events and characterizing the statistics of transition behaviors in stochastic...     

三峡水库岸边排污的特性及数值模拟研究

数值模拟是研究和解决三峡水库污水岸边排污的重要手段之一．针对三峡水库岸边污水排放的特点,分析并阐述了排污口附近的水流和污染物分布特性及其所带来的数值困难．基于这些分析,讨论了深度平均二维模型和不同分层三维模型在模拟三峡库区岸边排污问题中的优势和不足,为库区岸边侧向排污数值模型的进一步发展奠定了基础．     

Elementary bifurcations for a simple dynamical system under non-Gaussian Lévy noises

Nonlinear dynamical systems are sometimes under the influence of random fluctuations. It is desirable to examine possible bifurcations for stochastic dynamical systems when a parameter varies.     

Determining functionals for random partial differential equations

Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional random dynamical systems. In these applications the convergence condition of the trajectories of an infinite dimensional random dynamical system with respect to a finite set of linear functionals is assumed to be either in mean or exponential with respect to the convergence almost surely. In contrast to these ideas we introduce a convergence concept which is based on the convergence in probability. By this ansatz we get rid of the assumption of exponential convergence. In addition, setting the random terms to zero we obtain usual deterministic results.We apply our results to the 2D Navier-Stokes equations forced by a white noise.