Moment Closure - A Brief Review

Moment closure methods appear in myriad scientific disciplines in the modelling of complex systems. The goal is to achieve a closed form of a large, usually even infinite, set of coupled differential (or difference) equations. Each equation describes the evolution of one "moment", a suitable coarse-grained quantity computable from the full state space. If the system is too large for analytical and/or numerical methods, then one aims to reduce it by finding a moment closure relation expressing "higher-order moments" in terms of "lower-order moments". In this brief review, we focus on highlighting how moment closure methods occur in different contexts. We also conjecture via a geometric explanation why it has been difficult to rigorously justify many moment closure approximations although they work very well in practice.Comment: short survey paper (max 20 pages) for a broad audience in mathematics, physics, chemistry and quantitative biolog

Effect of peptide aerogel composite on silver nanoparticles as a catalyst for electrochemical CO₂ reduction

Electrochemical reduction of carbon dioxide (CO2RR) product distribution has been found to be dependent on several key factors, such as catalyst surface morphology, stability, and porosity. Metal-modified carbon-based materials have received a lot of attention in CO2RR. However, designing a highly active metal carbon catalyst for CO2RR utilizing low-cost chemical precursors remains a challenge. Here, a series of myristic acid-Phe-Phe peptide (MA-FF) aerogel materials containing graphene oxide (Gox) and Ag nanoparticles have been prepared for electrochemical CO2RR. The morphologies of the composites were studied by scanning electron microscopy (SEM), and their surface compositions were determined using X-ray photoelectron spectroscopy (XPS). While the peptide aerogel alone showed no catalytic activity for CO2 electroreduction, the addition of Ag nanoparticles results in a Faradaic efficiency (FE) of 46% for electroreduction of CO2 to CO at an overpotential of − 0.8 V vs. RHE. Incorporation of Gox in the aerogel increases the FE to 88% and allows CO2 reduction at a lower overpotential of − 0.7 V vs. RHE. Using highly porous peptide aerogels-Gox in addition to the metal active center provides an enhanced and new method for CO2 conversion using low environmental impact bio-based aerogels.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.ChemE/Materials for Energy Conversion and Storag

Some PDF integrals for self-similar turbulent flows

Self-similar solutions for the pdf integrals across the flow are considered for turbulent wakes and jets