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Statistical Mechanics of Liquids and Solutions: Intermolecular Forces, Structure and Surface Interactions
by Roland KjellanderThe statistical mechanical theory of liquids and solutions is a fundamental area of physical sciences with important implications for many industrial applications. This book shows how you can start from basic laws for the interactions and motions of microscopic particles and calculate how macroscopic systems of these particles behave, thereby explaining properties of matter at the scale that we perceive. Using this microscopic, molecular approach, the text emphasizes clarity of physical explanations for phenomena and mechanisms relevant to fluids, addressing the structure and behavior of liquids and solutions under various conditions. A notable feature is the author’s treatment of forces between particles that include nanoparticles, macroparticles, and surfaces. The book also provides an expanded, in-depth treatment of polar liquids and electrolytes.
Statistical Mechanics of Liquids and Solutions: Intermolecular Forces, Structure and Surface Interactions
by Roland KjellanderThe statistical mechanical theory of liquids and solutions is a fundamental area of physical sciences with important implications in other fields of science and industrial applications. Statistical Mechanics of Liquids and Solutions: Intermolecular Forces, Structure and Surface Interactions is the second in a series of two on this subject. While the first volume introduced equilibrium statistical mechanics in general and statistical mechanics of liquids and solutions at an introductory level, the present volume presents an advanced treatment of the subject and penetrates much deeper into liquid state theory.A major theme in both books is the intimate relationship between forces in a fluid and the fluid structure - a relationship that is paramount for the understanding of the subject of interactions in dense fluids. Using this microscopic, molecular approach, the text emphasizes clarity of physical explanations for phenomena and mechanisms relevant to fluids, addressing the structure and behavior of liquids and solutions under various conditions. A notable feature is the author's treatment of intermolecular interactions in liquids and solutions that include interactions between nanoparticles, macroparticles, and surfaces. The book provides an in-depth treatment of simple liquids, molecular fluids, particle dispersions, dense ionic fluids and electrolyte solutions with molecular solvent, both in the bulk and in confinement. It contains a unified exact treatment of electrolyte solutions, ionic liquids and polar fluids as well as approximate theories and applications.Statistical Mechanics of Liquids and Solutions will be an invaluable resource for graduate and postgraduate students in physics, chemistry, soft matter science, surface and colloid science and related fields, as well as professionals and instructors in those areas of science.
Statistical Mechanics of Neural Networks
by Haiping HuangThis book highlights a comprehensive introduction to the fundamental statistical mechanics underneath the inner workings of neural networks. The book discusses in details important concepts and techniques including the cavity method, the mean-field theory, replica techniques, the Nishimori condition, variational methods, the dynamical mean-field theory, unsupervised learning, associative memory models, perceptron models, the chaos theory of recurrent neural networks, and eigen-spectrums of neural networks, walking new learners through the theories and must-have skillsets to understand and use neural networks. The book focuses on quantitative frameworks of neural network models where the underlying mechanisms can be precisely isolated by physics of mathematical beauty and theoretical predictions. It is a good reference for students, researchers, and practitioners in the area of neural networks.
Statistical Mechanics of Superconductivity
by Takafumi KitaThis book provides a theoretical, step-by-step comprehensive explanation of superconductivity for undergraduate and graduate students who have completed elementary courses on thermodynamics and quantum mechanics. To this end, it adopts the unique approach of starting with the statistical mechanics of quantum ideal gases and successively adding and clarifying elements and techniques indispensible for understanding it. They include the spin-statistics theorem, second quantization, density matrices, the Bloch-De Dominicis theorem, the variational principle in statistical mechanics, attractive interaction and bound states. Ample examples of their usage are also provided in terms of topics from advanced statistical mechanics such as two-particle correlations of quantum ideal gases, derivation of the Hartree-Fock equations, and Landau's Fermi-liquid theory, among others. With these preliminaries, the fundamental mean-field equations of superconductivity are derived with maximum mathematical clarity based on a coherent state in terms of the Cooper-pair creation operator, a quasiparticle field for describing the excitation and the variational principle in statistical mechanics. They have the advantage that the phase coherence due to the Cooper-pair condensation can be clearly seen making the superfluidity comprehensible naturally. Subsequently, they are applied to homogeneous cases to describe the BCS theory for classic s-wave superconductors and its extension to the p-wave superfluidity of 3He. Later, the mean-field equations are simplified to the Eilenberger and Ginzburg-Landau equations so as to describe inhomogeneous superconductivity such as Abrikosov's flux-line lattice concisely and transparently. Chapters provide the latest studies on the quasiclassical theory of superconductivity and a discovery of p-wave superfluidity in liquid 3He. The book serves as a standard reference for advanced courses of statistical mechanics with exercises along with detailed answers.
Statistical Mechanics: A Concise Advanced Textbook (UNITEXT for Physics)
by Sergio CecottiThis textbook is based on lecture notes that the author delivered at Qiuzhen College (Tsinghua University), a Chinese institution known for its exceptionally talented mathematics students. The book's intended audience shapes its character. It introduces Statistical Mechanics from the ground up, offering a fully self-contained presentation that aims for mathematical precision. It distinguishes rigorous results from controlled approximations and provides physical insights into phenomena. Despite its concise nature (suited for a one-semester basic course), this book covers several topics typically not found in introductory texts. These include Shannon's information-theoretic interpretation of entropy, the gauge approach to order-disorder duality in the Ising model, the Yang-Lee theory, and the quantum dissipation-fluctuation theorem. Additionally, it explores frustrated and quenched systems, including an introduction to the celebrated Parisi solution of the Sherrington-Kirkpatrick model of spin glasses. The path integral formalism is extensively discussed from various perspectives to suit different applications. Chapter 2 approaches path integrals through the Feynman-Kac formula and second quantization. In Chapter 5, they are examined within the context of effective field theories like Landau-Ginzburg theory, while Chapter 6 delves into their connection with Brownian motion, Langevin stochastic differential equations, and Fokker-Planck diffusion PDEs. The book also explores the relationship between stochastic processes and supersymmetry. Various techniques for computing path integrals, especially functional determinants, are introduced throughout the relevant chapters, offering the most suitable computational tools for each application.
Statistical Mechanics: An Introductory Graduate Course (Graduate Texts in Physics)
by A. J. Berlinsky A. B. HarrisIn a comprehensive treatment of Statistical Mechanics from thermodynamics through the renormalization group, this book serves as the core text for a full-year graduate course in statistical mechanics at either the Masters or Ph.D. level. Each chapter contains numerous exercises, and several chapters treat special topics which can be used as the basis for student projects. The concept of scaling is introduced early and used extensively throughout the text. At the heart of the book is an extensive treatment of mean field theory, from the simplest decoupling approach, through the density matrix formalism, to self-consistent classical and quantum field theory as well as exact solutions on the Cayley tree. Proceeding beyond mean field theory, the book discusses exact mappings involving Potts models, percolation, self-avoiding walks and quenched randomness, connecting various athermal and thermal models. Computational methods such as series expansions and Monte Carlo simulations are discussed, along with exact solutions to the 1D quantum and 2D classical Ising models. The renormalization group formalism is developed, starting from real-space RG and proceeding through a detailed treatment of Wilson’s epsilon expansion. Finally the subject of Kosterlitz-Thouless systems is introduced from a historical perspective and then treated by methods due to Anderson, Kosterlitz, Thouless and Young. Altogether, this comprehensive, up-to-date, and engaging text offers an ideal package for advanced undergraduate or graduate courses or for use in self study.
Statistical Mechanics: From Thermodynamics to the Renormalization Group
by James H. LuscombeThis textbook provides a comprehensive, yet accessible, introduction to statistical mechanics. Crafted and class-tested over many years of teaching, it carefully guides advanced undergraduate and graduate students who are encountering statistical mechanics for the first time through this – sometimes – intimidating subject. The book provides a strong foundation in thermodynamics and the ensemble formalism of statistical mechanics. An introductory chapter on probability theory is included. Applications include degenerate Fermi systems, Bose-Einstein condensation, cavity radiation, phase transitions, and critical phenomena. The book concludes with a treatment of scaling theories and the renormalization group. In addition, it provides clear descriptions of how to understand the foundational mathematics and physics involved and includes exciting case studies of modern applications of the subject in physics and wider interdisciplinary areas. Key Features: Presents the subject in a clear and entertaining style which enables the author to take a sophisticated approach whilst remaining accessible Contains contents that have been carefully reviewed with a substantial panel to ensure that coverage is appropriate for a wide range of courses, worldwide Accompanied by volumes on thermodynamics and non-equilibrium statistical mechanics, which can be used in conjunction with this book, on courses which cover both thermodynamics and statistical mechanics
Statistical Mechanics: Fundamentals and Model Solutions
by Teunis C DorlasStatistical Mechanics: Fundamentals and Model Solutions, Second Edition Fully updated throughout and with new chapters on the Mayer expansion for classical gases and on cluster expansion for lattice models, this new edition of Statistical Mechanics: Fundamentals and Model Solutions provides a comprehensive introduction to equilibrium statistical mechanics for advanced undergraduate and graduate students of mathematics and physics. The author presents a fresh approach to the subject, setting out the basic assumptions clearly and emphasizing the importance of the thermodynamic limit and the role of convexity. With problems and solutions, the book clearly explains the role of models for physical systems, and discusses and solves various models. An understanding of these models is of increasing importance as they have proved to have applications in many areas of mathematics and physics. Features Updated throughout with new content from the field An established and well-loved textbook Contains new problems and solutions for further learning opportunity Author Professor Teunis C. Dorlas is at the Dublin Institute for Advanced Studies, Ireland.
Statistical Mechanics: Principles and Selected Applications
by Terrell L. HillBefore the publication of this standard, oft-cited book, there were few if any statistical-mechanics texts that incorporated reviews of both fundamental principles and recent developments in the field.In this volume, Professor Hill offers just such a dual presentation -- a useful account of basic theory and of its applications, made accessible in a comprehensive format. The book opens with concise, unusually clear introductory chapters on classical statistical mechanics, quantum statistical mechanics and the relation of statistical mechanics to thermodynamics. Then follows a wide-ranging, detailed examination of various applications. Chapter 4 deals with fluctuations. The fifth chapter treats the theory of imperfect gases and condensation, largely following Mayer's theory but also giving some new, alternative derivations and discussing in the final section Yang and Lee's theory. The sixth chapter is devoted to a discussion of distribution functions and the theory of the liquid state. Chapter 7 deals with nearest-neighbor (Ising) lattice statistics, while the last chapter discusses free-volume and hole theories of liquids and solids.Written primarily for graduate students and researchers in chemistry, physics and biology who already have some acquaintance with statistical mechanics, the book lends itself to use as a text for a second course in statistical mechanics, as a supplement to a first course or for self-study or reference. The level is neither introductory nor highly sophisticated; the author has generally emphasized material that is not available in other books. In addition, selected bibliographic references at the end of each chapter suggest supplementary reading.
Statistical Meso-Mechanics of Damage and Failure: Series Publication of Multiscale Mechanics
by Yilong Bai Mengfen Xia Fujiu KeThis book introduces a trans-scale framework necessary for the physical understanding of breakdown behaviors and presents some new paradigm to clarify the mechanisms underlying the trans-scale processes. The book, which is based on the interaction of mechanics and statistical physics, will help to deepen the understanding of how microdamage induces disaster and benefit the forecasting of the occurrence of catastrophic rupture. It offers notes and problems in each part as interesting background and illustrative exercises.Readers of the book would be graduate students, researchers, engineers working on civil, mechanical and geo-engineering, etc. However, people with various background but interested in disaster reduction and forecasting, like applied physics, geophysics, seismology, etc., may also be interested in the book.
Statistical Methods and Analyses for Medical Devices
by Scott A. PardoThis book provides a reference for people working in the design, development, and manufacturing of medical devices. While there are no statistical methods specifically intended for medical devices, there are methods that are commonly applied to various problems in the design, manufacturing, and quality control of medical devices. The aim of this book is not to turn everyone working in the medical device industries into mathematical statisticians; rather, the goal is to provide some help in thinking statistically, and knowing where to go to answer some fundamental questions, such as justifying a method used to qualify/validate equipment, or what information is necessary to support the choice of sample sizes.While, there are no statistical methods specifically designed for analysis of medical device data, there are some methods that seem to appear regularly in relation to medical devices. For example, the assessment of receiver operating characteristic curves is fundamental to development of diagnostic tests, and accelerated life testing is often critical for assessing the shelf life of medical device products. Another example is sensitivity/specificity computations are necessary for in-vitro diagnostics, and Taguchi methods can be very useful for designing devices. Even notions of equivalence and noninferiority have different interpretations in the medical device field compared to pharmacokinetics. It contains topics such as dynamic modeling, machine learning methods, equivalence testing, and experimental design, for example.This book is for those with no statistical experience, as well as those with statistical knowledgeable—with the hope to provide some insight into what methods are likely to help provide rationale for choices relating to data gathering and analysis activities for medical devices.
Statistical Methods and Modeling of Seismogenesis
by Nikolaos Limnios Eleftheria Papadimitriou George TsaklidisThe study of earthquakes is a multidisciplinary field, an amalgam of geodynamics, mathematics, engineering and more. The overriding commonality between them all is the presence of natural randomness. Stochastic studies (probability, stochastic processes and statistics) can be of different types, for example, the black box approach (one state), the white box approach (multi-state), the simulation of different aspects, and so on. This book has the advantage of bringing together a group of international authors, known for their earthquake-specific approaches, to cover a wide array of these myriad aspects. A variety of topics are presented, including statistical nonparametric and parametric methods, a multi-state system approach, earthquake simulators, post-seismic activity models, time series Markov models with regression, scaling properties and multifractal approaches, selfcorrecting models, the linked stress release model, Markovian arrival models, Poisson-based detection techniques, change point detection techniques on seismicity models, and, finally, semi-Markov models for earthquake forecasting.
Statistical Methods at the Forefront of Biomedical Advances
by Yolanda LarribaThis book presents novel statistics methods and reproducible software that helps to solve challenging problems in biomedicine. Specifically, it consists of a collection of 11 chapters contributed by some of the leading experts in the mathematical and statistical field which address new challenges in very disparate biomedical areas, such as genomics, cancer, circadian biology, microbiome, mental disorders, and more. The mathematical rigor is written in a user-friendly way to serve a general biomedical audience ranging from trainees or students to doctors, as well as scientific researchers, university departments, and PhD students.
Statistical Methods for Astronomical Data Analysis
by Asis Kumar Chattopadhyay Tanuka ChattopadhyayThis book introduces "Astrostatistics" as a subject in its own right with rewarding examples, including work by the authors with galaxy and Gamma Ray Burst data to engage the reader. This includes a comprehensive blending of Astrophysics and Statistics. The first chapter's coverage of preliminary concepts and terminologies for astronomical phenomenon will appeal to both Statistics and Astrophysics readers as helpful context. Statistics concepts covered in the book provide a methodological framework. A unique feature is the inclusion of different possible sources of astronomical data, as well as software packages for converting the raw data into appropriate forms for data analysis. Readers can then use the appropriate statistical packages for their particular data analysis needs. The ideas of statistical inference discussed in the book help readers determine how to apply statistical tests. The authors cover different applications of statistical techniques already developed or specifically introduced for astronomical problems, including regression techniques, along with their usefulness for data set problems related to size and dimension. Analysis of missing data is an important part of the book because of its significance for work with astronomical data. Both existing and new techniques related to dimension reduction and clustering are illustrated through examples. There is detailed coverage of applications useful for classification, discrimination, data mining and time series analysis. Later chapters explain simulation techniques useful for the development of physical models where it is difficult or impossible to collect data. Finally, coverage of the many R programs for techniques discussed makes this book a fantastic practical reference. Readers may apply what they learn directly to their data sets in addition to the data sets included by the authors.
Statistical Methods for Data Analysis in Particle Physics
by Luca ListaThis concise set of course-based notes provides the reader with the main concepts and tools to perform statistical analysis of experimental data, in particular in the field of high-energy physics (HEP). First, an introduction to probability theory and basic statistics is given, mainly as reminder from advanced undergraduate studies, yet also in view to clearly distinguish the Frequentist versus Bayesian approaches and interpretations in subsequent applications. More advanced concepts and applications are gradually introduced, culminating in the chapter on upper limits as many applications in HEP concern hypothesis testing, where often the main goal is to provide better and better limits so as to be able to distinguish eventually between competing hypotheses or to rule out some of them altogether. Many worked examples will help newcomers to the field and graduate students to understand the pitfalls in applying theoretical concepts to actual data.
Statistical Methods for Data Analysis in Particle Physics
by Luca ListaThis concise set of course-based notes provides the reader with the main concepts and tools to perform statistical analysis of experimental data, in particular in the field of high-energy physics (HEP). First, an introduction to probability theory and basic statistics is given, mainly as reminder from advanced undergraduate studies, yet also in view to clearly distinguish the Frequentist versus Bayesian approaches and interpretations in subsequent applications. More advanced concepts and applications are gradually introduced, culminating in the chapter on upper limits as many applications in HEP concern hypothesis testing, where often the main goal is to provide better and better limits so as to be able to distinguish eventually between competing hypotheses or to rule out some of them altogether. Many worked examples will help newcomers to the field and graduate students to understand the pitfalls in applying theoretical concepts to actual data.
Statistical Methods for Engineers and Scientists (Statistics: Textbooks and Monographs #144)
by Robert M. BetheaThis work details the fundamentals of applied statistics and experimental design, presenting a unified approach to data handling that emphasizes the analysis of variance, regression analysis and the use of Statistical Analysis System computer programs. This edition: discusses modern nonparametric methods; contains information on statistical process control and reliability; supplies fault and event trees; furnishes numerous additional end-of-chapter problems and worked examples; and more.
Statistical Methods for Food and Agriculture
by Filmore E BenderThis classic book will meet the needs of food and agricultural industries in both their research and business needs. Learn the fundamentals of applying statistics to the business and research needs in the food and agricultural industries. Statistical Methods for Food and Agriculture is a practical, hands-on resource that explores how statistics, a relatively recent development for science and business, facilitates the decision-making process. The range of techniques and applications explained and demonstrated in each of the four major sections of this volume provides a substantial course of study for those in business, government, and universities dealing with food, agriculture, and economics.Part I provides an introduction to the uses of statistics today, including basic concepts and definitions.Part II examines the statistical needs of the food researcher. The emphasis is on design of planned experiments, the analysis of data generated by planned experiments, and decision making in a research environment.Part III deals with statistical procedures that have a wide range of uses for the researcher and business analyst in both business and research situations.Part IV focuses on those statistical methods that have primarily a business application. This important volume is sufficiently detailed to enable the reader to learn and develop without outside assistance. References lead to more detailed presentations for those desiring additional specialized information, and helpful exercises at the end of each chapter permit the book?s use as a textbook as well.
Statistical Methods for Global Health and Epidemiology: Principles, Methods and Applications (ICSA Book Series in Statistics)
by Xinguang Chen Din Ding-Geng ChenThis book examines statistical methods and models used in the fields of global health and epidemiology. It includes methods such as innovative probability sampling, data harmonization and encryption, and advanced descriptive, analytical and monitory methods. Program codes using R are included as well as real data examples. Contemporary global health and epidemiology involves a myriad of medical and health challenges, including inequality of treatment, the HIV/AIDS epidemic and its subsequent control, the flu, cancer, tobacco control, drug use, and environmental pollution. In addition to its vast scales and telescopic perspective; addressing global health concerns often involves examining resource-limited populations with large geographic, socioeconomic diversities. Therefore, advancing global health requires new epidemiological design, new data, and new methods for sampling, data processing, and statistical analysis. This book provides global health researchers with methods that will enable access to and utilization of existing data. Featuring contributions from both epidemiological and biostatistical scholars, this book is a practical resource for researchers, practitioners, and students in solving global health problems in research, education, training, and consultation.
Statistical Methods for Imbalanced Data in Ecological and Biological Studies (SpringerBriefs in Statistics)
by Osamu Komori Shinto EguchiThis book presents a fresh, new approach in that it provides a comprehensive recent review of challenging problems caused by imbalanced data in prediction and classification, and also in that it introduces several of the latest statistical methods of dealing with these problems. The book discusses the property of the imbalance of data from two points of view. The first is quantitative imbalance, meaning that the sample size in one population highly outnumbers that in another population. It includes presence-only data as an extreme case, where the presence of a species is confirmed, whereas the information on its absence is uncertain, which is especially common in ecology in predicting habitat distribution. The second is qualitative imbalance, meaning that the data distribution of one population can be well specified whereas that of the other one shows a highly heterogeneous property. A typical case is the existence of outliers commonly observed in gene expression data, and another is heterogeneous characteristics often observed in a case group in case-control studies. The extension of the logistic regression model, maxent, and AdaBoost for imbalanced data is discussed, providing a new framework for improvement of prediction, classification, and performance of variable selection. Weights functions introduced in the methods play an important role in alleviating the imbalance of data. This book also furnishes a new perspective on these problem and shows some applications of the recently developed statistical methods to real data sets.
Statistical Methods for Materials Science: The Data Science of Microstructure Characterization
by Marc De Graef Jeffrey P. Simmons Lawrence F. Drummy Charles A. BoumanData analytics has become an integral part of materials science. This book provides the practical tools and fundamentals needed for researchers in materials science to understand how to analyze large datasets using statistical methods, especially inverse methods applied to microstructure characterization. It contains valuable guidance on essential topics such as denoising and data modeling. Additionally, the analysis and applications section addresses compressed sensing methods, stochastic models, extreme estimation, and approaches to pattern detection.
Statistical Methods for QTL Mapping (Chapman & Hall/CRC Computational Biology Series #53)
by Zehua ChenWhile numerous advanced statistical approaches have recently been developed for quantitative trait loci (QTL) mapping, the methods are scattered throughout the literature. Statistical Methods for QTL Mapping brings together many recent statistical techniques that address the data complexity of QTL mapping. After introducing basic genetics topics an
Statistical Methods for Spoken Dialogue Management
by Blaise ThomsonSpeech is the most natural mode of communication and yet attempts to build systems which support robust habitable conversations between a human and a machine have so far had only limited success. A key reason is that current systems treat speech input as equivalent to a keyboard or mouse, and behaviour is controlled by predefined scripts that try to anticipate what the user will say and act accordingly. But speech recognisers make many errors and humans are not predictable; the result is systems which are difficult to design and fragile in use. Statistical methods for spoken dialogue management takes a radically different view. It treats dialogue as the problem of inferring a user's intentions based on what is said. The dialogue is modelled as a probabilistic network and the input speech acts are observations that provide evidence for performing Bayesian inference. The result is a system which is much more robust to speech recognition errors and for which a dialogue strategy can be learned automatically using reinforcement learning. The thesis describes both the architecture, the algorithms needed for fast real-time inference over very large networks, model parameter estimation and policy optimisation. This ground-breaking work will be of interest both to practitioners in spoken dialogue systems and to cognitive scientists interested in models of human behaviour.
Statistical Methods in Biomarker and Early Clinical Development
by Liang Fang Cheng SuThis contributed volume offers a much-needed overview of the statistical methods in early clinical drug and biomarker development. Chapters are written by expert statisticians with extensive experience in the pharmaceutical industry and regulatory agencies. Because of this, the data presented is often accompanied by real world case studies, which will help make examples more tangible for readers. The many applications of statistics in drug development are covered in detail, making this volume a must-have reference.Biomarker development and early clinical development are the two critical areas on which the book focuses. By having the two sections of the book dedicated to each of these topics, readers will have a more complete understanding of how applying statistical methods to early drug development can help identify the right drug for the right patient at the right dose. Also presented are exciting applications of machine learning and statistical modeling, along with innovative methods and state-of-the-art advances, making this a timely and practical resource.This volume is ideal for statisticians, researchers, and professionals interested in pharmaceutical research and development. Readers should be familiar with the fundamentals of statistics and clinical trials.
Statistical Methods in Human Genetics (Indian Statistical Institute Series)
by Indranil Mukhopadhyay Partha Pratim MajumderThis book provides an overview of statistical concepts and basic methodology for the study of genetics of human traits and diseases. It attempts to provide a step-by-step description of problem identification, study design, methodology of data collection, data exploration, data summarization and visualization, and more advanced analytical methods for inferring genetic underpinnings of human phenotypes. The book provides codes in R programming language for implementation of most of the statistical methods described, which will enable practitioners to perform analysis of data on their own, without having to mold the data to fit the requirements of commercial statistical packages. Useful to anyone engaged in studies to understand and manage good health, the book is a useful guide for sustainable development of humankind. Primarily intended for practicing biologists especially those who carry out quantitative biological research, in particular, human geneticists, the book is also helpful in classroom teaching.