Computing and Analysing Energy Minimisation Problems in Liquid Crystals

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How does one numerically analyse different phases of liquid crystals? With the help of some open-source libraries, what can we do in exploiting the mathematical models of liquid crystals and numerical aspects of their typical defects? There are many excellent books on liquid crystals, but none on their numerics to the knowledge of the author. This book presents some of the latest work on numerical investigations of liquid crystals, addressing some mathematical modelling and numerical problems. This book consists of three major parts, each of which focuses on different problems for different phases of liquid crystals: nematics and cholesterics, ferronematics and smectics. The associated topics include robust solvers for cholesterics, multiple solutions for ferronematics, and mathematical modelling theory for smectics, etc. This interdisciplinary book can be helpful in utilising the open-source libraries Firedrake (for solving problems using finite element methods) and Defcon (for computing multiple solutions) to solve general energy minimisation problems. Sample Chapter(s) Preface Chapter 1: Introduction Chapter 2: A Mathematical Model of Nematics and Cholesterics Contents: Introduction Nematic and Cholesteric Liquid Crystals: A Mathematical Model of Nematics and Cholesterics A Robust Multigrid Algorithm for the Augmented Director Block Numerical Experiments for Nematics and Cholesterics Ferronematic Liquid Crystals: A Mathematical Model of Ferronematics Computing Multiple Solutions Using Deflation Numerical Verifications for Ferronematics Smectic Liquid Crystals: A Mathematical Model of Smectics Finite Element Discretisation Numerical Experiments for Smectics Conclusions and Perspectives: Summary and Conclusions Appendices: Stability of the Newton System Equilibrium Equations in Two Dimensions Readership: Advanced undergraduate and graduate students interested in numerical modelling of liquid crystals; researchers in the fields of mathematical theories and numerical aspects in liquid crystals.

Heterogeneous Nanocatalysis for Energy and Environmental Sustainability, Volume 1: Energy Applications (1版)

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【簡介】 An essential companion for catalysis researchers and professionals studying economically viable and eco-friendly catalytic strategies for energy conversionIn the two-volume Heterogeneous Nanocatalysis for Energy and Environmental Sustainability, a team of distinguished researchers deliver a comprehensive discussion of fundamental concepts in, and practical applications of, heterogeneous nanocatalysis for alternative energy production, biomass conversion, solar energy, green fuels, H2 production, fuel cells, electrochemical energy conversion processes, CO2 conversion, clean water, and environmental protection.The volumes cover the design and catalytic performance of various nanocatalysts, including nanosized metals and metal oxides, supported metal nanoparticles, inverse oxide-metal nanocatalysts, core-shell nanocatalysts, nanoporous zeolites, nanocarbon composites, and metal oxides in confined spaces. Each chapter contains a critical discussion of the opportunities and challenges posed by the use of nanosized catalysts for practical applications.Volume 1 - Energy Applications focuses on the conversion of renewable energy (biomass/solar) into green fuels and chemicals, ammonia synthesis, clean hydrogen production, and electrochemical energy conversion processes using a variety of nanosized catalysts.It also offers: A thorough introduction to heterogeneous catalysis and nanocatalysis, as well as a discussion of catalytic active sites at nano-scale rangeComprehensive explorations of the methods for control and activation of nanosized catalystsPractical discussions of C3N4-based nanohybrid catalysts for solar hydrogen production via water splittingNanosized catalysts in visible light photocatalysis for sustainable organic synthesisApplications of MXenes in electrocatalysisPerfect for researchers, postgraduate students, chemists, and engineers interested in heterogeneous catalysis and nanocatalysis, Heterogeneous Nanocatalysis for Energy and Environmental Sustainability will also earn a place in the libraries of professionals working in alternative energy production, biomass conversion, solar energy, green fuels, H2 production, fuel cells, electrochemical energy conversion processes, CO2 conversion, clean water, and environmental protection.