Download or read book The Poisson Boltzmann Equation written by Ralf Blossey and published by Springer Nature. This book was released on 2023-02-23 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief book introduces the Poisson-Boltzmann equation in three chapters that build upon one another, offering a systematic entry to advanced students and researchers. Chapter one formulates the equation and develops the linearized version of Debye-Hückel theory as well as exact solutions to the nonlinear equation in simple geometries and generalizations to higher-order equations. Chapter two introduces the statistical physics approach to the Poisson-Boltzmann equation. It allows the treatment of fluctuation effects, treated in the loop expansion, and in a variational approach. First applications are treated in detail: the problem of the surface tension under the addition of salt, a classic problem discussed by Onsager and Samaras in the 1930s, which is developed in modern terms within the loop expansion, and the adsorption of a charged polymer on a like-charged surface within the variational approach. Chapter three finally discusses the extension of Poisson-Boltzmann theory to explicit solvent. This is done in two ways: on the phenomenological level of nonlocal electrostatics and with a statistical physics model that treats the solvent molecules as molecular dipoles. This model is then treated in the mean-field approximation and with the variational method introduced in Chapter two, rounding up the development of the mathematical approaches of Poisson-Boltzmann theory. After studying this book, a graduate student will be able to access the research literature on the Poisson-Boltzmann equation with a solid background.
Download or read book Molecular Biophysics written by Michel Daune and published by Oxford University Press, USA. This book was released on 1999 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new textbook offers a comprehensive introduction to the molecular physics of biological systems: it seeks to explain how the laws and concepts of physics apply to the living world at the molecular and subcellular level, with an emphasis on electrical and dynamical behaviour. The book is organized into five parts: * conformation of biopolymers * dynamics of biopolymers * hydration of biopolymers * biopolymers as polyelectrolytes *association between molecules The author adopts a multi-disciplinary approach and limits mathematics only to what is strictly necessary for the development of the subject. The text should be suitable for students from a wide range of backgrounds in biology, physics or chemistry taking advanced courses in molecular biophysics or biophysical chemistry.
Download or read book The Boltzmann Equation written by E.G.D. Cohen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 647 pages. Available in PDF, EPUB and Kindle. Book excerpt: In,1872, Boltzmann published a paper which for the first time provided a precise mathematical basis for a discussion of the approach to equilibrium. The paper dealt with the approach to equilibrium of a dilute gas and was based on an equation - the Boltzmann equation, as we call it now - for the velocity distribution function of such ~ gas. The Boltzmann equation still forms the basis of the kinetic theory of gases and has proved fruitful not only for the classical gases Boltzmann had in mind, but als- if properly generalized - for the electron gas in a solid and the excitation gas in a superfluid. Therefore it was felt by many of us that the Boltzmann equation was of sufficient interest, even today, to warrant a meeting, in which a review of its present status would be undertaken. Since Boltzmann had spent a good part of his life in Vienna, this city seemed to be a natural setting for such a meeting. The first day was devoted to historical lectures, since it was generally felt that apart from their general interest, they would furnish a good introduction to the subsequent scientific sessions. We are very much indebted to Dr. D.
Download or read book Kinetic Boltzmann Vlasov and Related Equations written by Alexander Sinitsyn and published by Elsevier. This book was released on 2011-06-17 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boltzmann and Vlasov equations played a great role in the past and still play an important role in modern natural sciences, technique and even philosophy of science. Classical Boltzmann equation derived in 1872 became a cornerstone for the molecular-kinetic theory, the second law of thermodynamics (increasing entropy) and derivation of the basic hydrodynamic equations. After modifications, the fields and numbers of its applications have increased to include diluted gas, radiation, neutral particles transportation, atmosphere optics and nuclear reactor modelling. Vlasov equation was obtained in 1938 and serves as a basis of plasma physics and describes large-scale processes and galaxies in astronomy, star wind theory. This book provides a comprehensive review of both equations and presents both classical and modern applications. In addition, it discusses several open problems of great importance. Reviews the whole field from the beginning to today Includes practical applications Provides classical and modern (semi-analytical) solutions
Download or read book Plasma Electronics written by Toshiaki Makabe and published by CRC Press. This book was released on 2006-03-27 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: Without plasma processing techniques, recent advances in microelectronics fabrication would not have been possible. But beyond simply enabling new capabilities, plasma-based techniques hold the potential to enhance and improve many processes and applications. They are viable over a wide range of size and time scales, and can be used for deposition,
Download or read book Applied Colloid and Surface Chemistry written by Richard M. Pashley and published by John Wiley & Sons. This book was released on 2005-07-15 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applied Colloid and Surface Chemistry is a broadintroduction to this interdisciplinary field. Taking a genuinelyapplied approach, with applications drawn from a wide range ofindustries, this book will meet the demands of the student andprofessional currently working in the field. The text includes keynote sections written by practicingindustrial research scientists, bringing to the reader a wealth ofreal industrial examples. These examples range from water treatmentthrough to soil management as well as examples taken from thecoatings and photographic industries. To aid accessibility, some ofthe more demanding mathematical derivations are separated from themain text, enabling them to be avoided as required. With carefully structured chapters, starting with learningobjectives, and containing tutorial questions with answers andexplanatory notes, this text is invaluable for undergraduatestaking a first course on colloid and surface chemistry. This bookwill also be suitable to postgraduates and professionals, who needan up-to-date account of the subject.
Download or read book Reduced Basis Methods for Partial Differential Equations written by Alfio Quarteroni and published by Springer. This book was released on 2015-08-19 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a basic introduction to reduced basis (RB) methods for problems involving the repeated solution of partial differential equations (PDEs) arising from engineering and applied sciences, such as PDEs depending on several parameters and PDE-constrained optimization. The book presents a general mathematical formulation of RB methods, analyzes their fundamental theoretical properties, discusses the related algorithmic and implementation aspects, and highlights their built-in algebraic and geometric structures. More specifically, the authors discuss alternative strategies for constructing accurate RB spaces using greedy algorithms and proper orthogonal decomposition techniques, investigate their approximation properties and analyze offline-online decomposition strategies aimed at the reduction of computational complexity. Furthermore, they carry out both a priori and a posteriori error analysis. The whole mathematical presentation is made more stimulating by the use of representative examples of applicative interest in the context of both linear and nonlinear PDEs. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text. The book will be ideal for upper undergraduate students and, more generally, people interested in scientific computing. All these pseudocodes are in fact implemented in a MATLAB package that is freely available at https://github.com/redbkit
Download or read book Deterministic Solvers for the Boltzmann Transport Equation written by Sung-Min Hong and published by Springer Science & Business Media. This book was released on 2011-07-31 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book covers all aspects from the expansion of the Boltzmann transport equation with harmonic functions to application to devices, where transport in the bulk and in inversion layers is considered. The important aspects of stabilization and band structure mapping are discussed in detail. This is done not only for the full band structure of the 3D k-space, but also for the warped band structure of the quasi 2D hole gas. Efficient methods for building the Schrödinger equation for arbitrary surface or strain directions, gridding of the 2D k-space and solving it together with the other two equations are presented.
Download or read book The Cauchy Problem in Kinetic Theory written by Robert T. Glassey and published by SIAM. This book was released on 1996-01-01 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies the basic equations of kinetic theory in all of space, and contains up-to-date, state-of-the-art treatments of initial-value problems for the major kinetic equations. This is the only existing book to treat Boltzmann-type problems and Vlasov-type problems together. Although describing very different phenomena, these equations share the same streaming term.
Download or read book The Optimal Homotopy Asymptotic Method written by Vasile Marinca and published by Springer. This book was released on 2015-04-02 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book emphasizes in detail the applicability of the Optimal Homotopy Asymptotic Method to various engineering problems. It is a continuation of the book “Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches”, published at Springer in 2011 and it contains a great amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines and so on. The main structure of the book consists of 5 chapters. The first chapter is introductory while the second chapter is devoted to a short history of the development of homotopy methods, including the basic ideas of the Optimal Homotopy Asymptotic Method. The last three chapters, from Chapter 3 to Chapter 5, are introducing three distinct alternatives of the Optimal Homotopy Asymptotic Method with illustrative applications to nonlinear dynamical systems. The third chapter deals with the first alternative of our approach with two iterations. Five applications are presented from fluid mechanics and nonlinear oscillations. The Chapter 4 presents the Optimal Homotopy Asymptotic Method with a single iteration and solving the linear equation on the first approximation. Here are treated 32 models from different fields of engineering such as fluid mechanics, thermodynamics, nonlinear damped and undamped oscillations, electrical machines and even from physics and biology. The last chapter is devoted to the Optimal Homotopy Asymptotic Method with a single iteration but without solving the equation in the first approximation.
Download or read book Surface Forces written by Nikolai V. Churaev and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to long-range surface forces sig nificant far beyond a single monolayer and felt over tens or even hundreds of molecular layers adjacent to an interface. The transi tion from the concept of short-range effects that reigned earlier to the concept of long-range forces simultaneously signified the transition from a two-dimensional world to a three-dimensional one, incomparably richer in physicochemical phenomena. This transition took many years and evolved through many steps. It began with the Gouy-Chapman theory of diffuse ionic atmospheres, which together with London's theory of molecular forces was used as a basis for the development (beginning in 1937) of the DLVO theory of stability of lyophobic colloids. Further elaboration of the theory involved the introduction of new types of force, and a generalization (in 1954) to the case of interaction between unlike particles (hetero coagulation). This theory is fundamental in such large-scale prac tical problems as flotation, water treatment, dyeing, soil science, microbiology, and interaction between biological cells. This book is the first comprehensive monograph devoted to sur face forces. This fact makes it easier to attract the reader's interest; yet, the reader's demands become all the more difficult to satisfy completely. Indeed, the research that we review and analyze here covers about 50 years of work. Much data has been amassed, so that the main problem was a careful selection and an alysis.
Download or read book Certified Reduced Basis Methods for Parametrized Partial Differential Equations written by Jan S Hesthaven and published by Springer. This book was released on 2015-08-20 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.
Download or read book Computer Simulation Using Particles written by R.W Hockney and published by CRC Press. This book was released on 2021-03-24 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer simulation of systems has become an important tool in scientific research and engineering design, including the simulation of systems through the motion of their constituent particles. Important examples of this are the motion of stars in galaxies, ions in hot gas plasmas, electrons in semiconductor devices, and atoms in solids and liquids. The behavior of the system is studied by programming into the computer a model of the system and then performing experiments with this model. New scientific insight is obtained by observing such computer experiments, often for controlled conditions that are not accessible in the laboratory. Computer Simulation using Particles deals with the simulation of systems by following the motion of their constituent particles. This book provides an introduction to simulation using particles based on the NGP, CIC, and P3M algorithms and the programming principles that assist with the preparations of large simulation programs based on the OLYMPUS methodology. It also includes case study examples in the fields of astrophysics, plasmas, semiconductors, and ionic solids as well as more detailed mathematical treatment of the models, such as their errors, dispersion, and optimization. This resource will help you understand how engineering design can be assisted by the ability to predict performance using the computer model before embarking on costly and time-consuming manufacture.
Download or read book Many Body Effects and Electrostatics in Biomolecules written by Qiang Cui and published by CRC Press. This book was released on 2016-03-30 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: As computational hardware continues to develop at a rapid pace, quantitative computations are playing an increasingly essential role in the study of biomolecular systems. One of the most important challenges that the field faces is to develop the next generation of computational models that strike the proper balance of computational efficiency and accuracy, so that the problems of increasing complexity can be tackled in a systematic and physically robust manner. In particular, properly treating intermolecular interactions is fundamentally important for the reliability of all computational models. In this book, contributions by leading experts in the area of biomolecular simulations discuss cutting-edge ideas regarding effective strategies to describe many-body effects and electrostatics at quantum, classical, and coarse-grained levels. The goal of the book is to not only provide an up-to-date snapshot of the current simulation field but also stimulate exchange of ideas across different sub-fields of modern computational (bio)chemistry. The text will be a useful reference for the biomolecular simulation community and help attract talented young students into this exciting frontier of research.
Download or read book Theory of Solutions written by John G. Kirkwood and published by CRC Press. This book was released on 2001-12 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fourier Analysis and Its Applications written by G. B. Folland and published by American Mathematical Soc.. This book was released on 2009 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the theory and applications of Fourier series and integrals, eigenfunction expansions, and related topics, on a level suitable for advanced undergraduates. It includes material on Bessel functions, orthogonal polynomials, and Laplace transforms, and it concludes with chapters on generalized functions and Green's functions for ordinary and partial differential equations. The book deals almost exclusively with aspects of these subjects that are useful in physics and engineering, and includes a wide variety of applications. On the theoretical side, it uses ideas from modern analysis to develop the concepts and reasoning behind the techniques without getting bogged down in the technicalities of rigorous proofs.
Download or read book Structure and Dynamics of Membranes written by R. Lipowsky and published by Elsevier. This book was released on 1995-06-15 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first volume of the Handbook deals with the amazing world of biomembranes and lipid bilayers. Part A describes all aspects related to the morphology of these membranes, beginning with the complex architecture of biomembranes, continues with a description of the bizarre morphology of lipid bilayers and concludes with technological applications of these membranes. The first two chapters deal with biomembranes, providing an introduction to the membranes of eucaryotes and a description of the evolution of membranes. The following chapters are concerned with different aspects of lipids including the physical properties of model membranes composed of lipid-protein mixtures, lateralphase separation of lipids and proteins and measurement of lipid-protein bilayer diffusion. Other chapters deal with the flexibility of fluid bilayers, the closure of bilayers into vesicles which attain a large variety of different shapes, and applications of lipid vesicles and liposomes. Part B covers membrane adhesion, membrane fusion and the interaction of biomembranes withpolymer networks such as the cytoskeleton. The first two chapters of this part discuss the generic interactions of membranes from the conceptual point of view. The following two chapters summarize the experimental work on two different bilayer systems. The next chapter deals with the process ofcontact formation, focal bounding and macroscopic contacts between cells. The cytoskeleton within eucaryotic cells consists of a network of relatively stiff filaments of which three different types of filaments have been identified. As explained in the next chapter much has been recently learned aboutthe interaction of these filaments with the cell membrane. The final two chapters deal with membrane fusion.
