Computing and Analysing Energy Minimisation Problems in Liquid Crystals

類似書籍推薦給您

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.

Analyzing American Democracy: Politics and Political Science 5th 2024 (5版)

類似書籍推薦給您

Providing the tools for critical thinking, the fifth edition of Analyzing American Democracy: Politics and Political Science relies on statistical analysis, constitutional scholarship, and theoretical foundations to introduce the structure, process, and outcomes of the U.S. political system. Interpretation and implications of the 2022 mid-term elections and full results of the 2020 census are included, as are discussions of:: the January 6th commission, major developments in the Supreme Court, the Covid-19 pandemic, the Russian invasion of Ukraine, and other key political events that shape domestic, foreign, judicial, and economic policies. For introductory courses in American government, this text covers theory and methods as well. New to the Fifth Edition • New and updated statistical data reflecting the 2020 census and the 2022 midterm elections, and discussions of the implications of the data and the results. • Offers a retrospective analysis of the entire Trump presidency and the first years of the Biden presidency. • Examines contemporary questions of social justice and anticipates upcoming challenges to voting rights, affirmative action policies, health care and reproductive rights, and protections for ethnic minorities and the LGBT community. • Previews the policy implications of an increasingly partisan Supreme Court, recaps the controversial recent decisions on health care, abortion, and environmental policy, and covers the historic confirmation of new justice Ketanji Brown-Jackson.