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Mathematical analysis of partial differential equations modeling electrostatic MEMS
Esposito, PierpaoloNew York : Courant Institute of Mathematical Sciences ; Providence, R.I. : American Mathematical Society, c2010."Micro- and nanoelectromechanical systems (MEMS and NEMS), which combine electronics with miniature-size mechanical devices, are essential components of modern technology. It is the mathematical model describing 'electrostatically actuated' MEMS that is addressed in this monograph. Even the simplified models that the authors deal with still lead to very interesting second- and fourth-order nonlinear elliptic equations (in the stationary case) and to nonlinear parabolic equations (in the dynamic case). While nonlinear eigenvalue problems - where the stationary MEMS models fit - are a well-developed field of PDEs, the type of inverse square nonlinearity that appears here helps shed a new light on the class of singular supercritical problems and their specific challenges. Besides the practical considerations, the model is a rich source of interesting mathematical phenomena. Numerics, formal asymptotic analysis, and ODE methods give lots of information and point to many conjectures. However, even in the simplest idealized versions of electrostatic MEMS, one essentially needs the full available arsenal of modern PDE techniques to do the required rigorous mathematical analysis, which is the main objective of this volume. This monograph could therefore be used as an advanced graduate text for a motivational introduction to many recent methods of nonlinear analysis and PDEs through the analysis of a set of equations that have enormous practical significance."--Publisher's description.Micro- and nanoelectromechanical systems (MEMS and NEMS), which combine electronics with miniature-size mechanical devices, are essential components of modern technology. It is the mathematical model describing 'electrostatically actuated' MEMS that is addressed in this monograph. Even the simplified models that the authors deal with still lead to very interesting second- and fourth-order nonlinear elliptic equations (in the stationary case) and to nonlinear parabolic equations (in the dynamic case). While nonlinear eigenvalue problems - where the stationary MEMS models fit - are a well-developed field of PDEs, the type of inverse square nonlinearity that appears here helps shed a new light on the class of singular supercritical problems and their specific challenges. Besides the practical considerations, the model is a rich source of interesting mathematical phenomena. Numerics, formal asymptotic analysis, and ODE methods give lots of information and point to many conjectures. However, even in the simplest idealized versions of electrostatic MEMS, one essentially needs the full available arsenal of modern PDE techniques to do the required rigorous mathematical analysis, which is the main objective of this volume. This monograph could therefore be used as an advanced graduate text for a motivational introduction to many recent methods of nonlinear analysis and PDEs through the analysis of a set of equations that have enormous practical significance.
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Data science and social research : epistemology, methods, technology and applications
Cham : Springer International Publishing, 2017.This edited volume lays the groundwork for Social Data Science, addressing epistemological issues, methods, technologies, software and applications of data science in the social sciences. It presents data science techniques for the collection, analysis and use of both online and offline new (big) data in social research and related applications. Among others, the individual contributions cover topics like social media, learning analytics, clustering, statistical literacy, recurrence analysis and network analysis. Data science is a multidisciplinary approach based mainly on the methods of statistics and computer science, and its aim is to develop appropriate methodologies for forecasting and decision-making in response to an increasingly complex reality often characterized by large amounts of data (big data) of various types (numeric, ordinal and nominal variables, symbolic data, texts, images, data streams, multi-way data, social networks etc.) and from diverse sources. This book presents selected papers from the international conference on Data Science & Social Research, held in Naples, Italy in February 2016, and will appeal to researchers in the social sciences working in academia as well as in statistical institutes and offices.--This edited volume lays the groundwork for Social Data Science, addressing epistemological issues, methods, technologies, software and applications of data science in the social sciences. It presents data science techniques for the collection, analysis and use of both online and offline new (big) data in social research and related applications. Among others, the individual contributions cover topics like social media, learning analytics, clustering, statistical literacy, recurrence analysis and network analysis. Data science is a multidisciplinary approach based mainly on the methods of statistics and computer science, and its aim is to develop appropriate methodologies for forecasting and decision-making in response to an increasingly complex reality often characterized by large amounts of data (big data) of various types (numeric, ordinal and nominal variables, symbolic data, texts, images, data streams, multi-way data, social networks etc.) and from diverse sources. This book presents selected papers from the international conference on Data Science & Social Research, held in Naples, Italy in February 2016, and will appeal to researchers in the social sciences working in academia as well as in statistical institutes and offices.
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