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Statistical Thermodynamics
by Normand M. LaurendeauStatistical Thermodynamics: Fundamentals and Applications discusses the fundamentals and applications of statistical thermodynamics for beginning graduate students in the engineering sciences. Building on the Maxwell-Boltzmann method of step-by-step development of the subject, this book makes few presumptions concerning students, previous exposure to statistics, quantum mechanics or spectroscopy. The book begins with the fundamentals of statistical thermodynamics, pauses to recover needed knowledge from quantum mechanics and spectroscopy, and then moves on to applications involving ideal gases, the solid state and radiation. A full introduction to kinetic theory is provided, including its applications to transport phenomena and chemical kinetics. Modern applications, such as laser-based diagnostics, are also discussed. Each chapter is carefully written to address student difficulties in learning this challenging subject, which is fundamental to combustion, propulsion, transport phenomena, spectroscopic measurements and nanotechnology. Students are made comfortable with their new knowledge by the inclusion of both example and prompted homework problems.
Statistical Thermodynamics Of Surfaces, Interfaces, And Membranes (Frontiers in Physics #Vol. 90)
by Samuel SafranUnderstanding the structural and thermodynamic properties of surfaces, interfaces, and membranes is important for both fundamental and practical reasons. Important applications include coatings, dispersants, encapsulating agents, and biological materials. Soft materials, important in the development of new materials and the basis of many biological systems, cannot be designed using trial and error methods due to the multiplicity of components and parameters. While these systems can sometimes be analyzed in terms of microscopic mixtures, it is often conceptually simpler to regard them as dispersions and to focus on the properties of the internal interfaces found in these systems. The basic physics centers on the properties of quasi-two-dimensional systems embedded in the three-dimensional world, thus exhibiting phenomena that do not exist in bulk materials. This approach is the basis behind the theoretical presentation of Statistical Thermodynamics of Surfaces, Interfaces, and Membranes. The approach adapted allows one to treat the rich diversity of phenomena investigated in the field of soft matter physics (including both colloid/interface science as well as the materials and macromolecular aspects of biological physics) such as interfacial tension, the roughening transition, wetting, interactions between surfaces, membrane elasticity, and self-assembly. Presented as a set of lecture notes, this book is aimed at physicists, physical chemists, biological physicists, chemical engineers, and materials scientists who are interested in the statistical mechanics that underlie the macroscopic, thermodynamic properties of surfaces, interfaces, and membranes. This paperback edition contains all the material published in the original hard-cover edition as well as additional clarifications and explanations.
Statistical Thermodynamics and Stochastic Kinetics
by Yiannis N. KaznessisPresenting the key principles of thermodynamics from a microscopic point of view, this book provides engineers with the knowledge they need to apply thermodynamics and solve engineering challenges at the molecular level. It clearly explains the concepts of entropy and free energy, emphasizing key ideas used in equilibrium applications, whilst stochastic processes, such as stochastic reaction kinetics, are also covered. It provides a classical microscopic interpretation of thermodynamic properties, which is key for engineers, rather than focusing on more esoteric concepts of statistical mechanics and quantum mechanics. Coverage of molecular dynamics and Monte Carlo simulations as natural extensions of the theoretical treatment of statistical thermodynamics is also included, teaching readers how to use computer simulations and thus enabling them to understand and engineer the microcosm. Featuring many worked examples and over 100 end-of-chapter exercises, it is ideal for use in the classroom as well as for self-study.
Statistical Thermodynamics and Stochastic Kinetics
by Yiannis N. KaznessisPresenting the key principles of thermodynamics from a microscopic point of view, this book provides engineers with the knowledge they need to apply thermodynamics and solve engineering challenges at the molecular level. It clearly explains the concepts of entropy and free energy, emphasizing key ideas used in equilibrium applications, whilst stochastic processes, such as stochastic reaction kinetics, are also covered. It provides a classical microscopic interpretation of thermodynamic properties, which is key for engineers, rather than focusing on more esoteric concepts of statistical mechanics and quantum mechanics. Coverage of molecular dynamics and Monte Carlo simulations as natural extensions of the theoretical treatment of statistical thermodynamics is also included, teaching readers how to use computer simulations and thus enabling them to understand and engineer the microcosm. Featuring many worked examples and over 100 end-of-chapter exercises, it is ideal for use in the classroom as well as for self-study.
Statistical Thermodynamics for Pure and Applied Sciences: Statistical Thermodynamics
by Frederick Richard McCourtThis textbook concerns thermal properties of bulk matter and is aimed at advanced undergraduate or first-year graduate students in a range of programs in science or engineering. It provides an intermediate level presentation of statistical thermodynamics for students in the physical sciences (chemistry, nanosciences, physics) or related areas of applied science/engineering (chemical engineering, materials science, nanotechnology engineering), as they are areas in which statistical mechanical concepts play important roles. The book enables students to utilize microscopic concepts to achieve a better understanding of macroscopic phenomena and to be able to apply these concepts to the types of sub-macroscopic systems encountered in areas of nanoscience and nanotechnology.
Statistical Thermodynamics: A Course Of Seminar Lectures Delivered In January (Dover Books On Physics Series)
by Erwin SchrodingerIn this concise volume, one of the founder of quantum mechanics and one of the greatest theoretical physicists of the century (Nobel laureate, 1933) attempts to develop a simple, unified standard method of dealing with all cases of statistical thermodynamics (classical, quantum, Bose-Einstein, Fermi-Dirac, etc.)The level of discussion is relatively advanced. As Professor Schrödinger remarks in the Introduction: "It is not a first introduction for newcomers to the subject, but rather a 'repetitorium.' The treatment of those topics which are to be found in every one of a hundred text-books is severely condensed; on the other hand, vital points which are usually passed over in all but the large monographs (such as Fowler's and Tolman's) are dealt with at greater level."
Statistical Thermodynamics: An Information Theory Approach
by Christopher AubinStatistical Thermodynamics An accessible and rigorous approach to thermodynamics and statistical mechanics In Statistical Thermodynamics: An Information Theory Approach, distinguished physicist Dr. Christopher Aubin delivers an accessible and comprehensive treatment of the subject from a statistical mechanics perspective. The author discusses the most challenging concept, entropy, using an information theory approach, allowing readers to build a solid foundation in an oft misunderstood and critically important physics concept. This text offers readers access to complimentary online materials, including animations, simple code, and more, that supplement the discussions of complex topics in the book. It provides calculations not usually provided in comparable textbooks that demonstrate how to perform the mathematics of thermodynamics in a systematic way. Readers will also find authoritative explorations of relevant theory accompanied by clear examples of applications and experiments, as well as: A brief introduction to information theory, as well as discussions of statistical systems, phase space, and the Microcanonical Ensemble Comprehensive explorations of the laws and mathematics of thermodynamics, as well as free expansion, Joule-Thomson expansion, heat??engines, and refrigerators Practical discussions of classical and quantum statistics, quantum ideal gases, and blackbody radiation Fulsome treatments of novel topics, including Bose-Einstein condensation, the Fermi gas, and black hole thermodynamics Perfect for upper-level undergraduate students studying statistical mechanics and thermodynamics, Statistical Thermodynamics: An Information Theory Approach provides an alternative and accessible approach to the subject.
Statistical Thermodynamics: Basics and Applications to Chemical Systems
by Iwao TeraokaThis textbook introduces chemistry and chemical engineering students to molecular descriptions of thermodynamics, chemical systems, and biomolecules. Equips students with the ability to apply the method to their own systems, as today's research is microscopic and molecular and articles are written in that language Provides ample illustrations and tables to describe rather difficult concepts Makes use of plots (charts) to help students understand the mathematics necessary for the contents Includes practice problems and answers
Statistical Thermodynamics: Understanding the Properties of Macroscopic Systems
by Lukong Cornelius Fai Gary Matthew WysinPresenting a look at the modern evolution of statistical thermodynamics, this book provides a detailed overview of the statistical principles used to obtain the physical and thermodynamic properties of macroscopic systems. Going further than many advanced textbooks, it includes Bose-Einstein, Fermi-Dirac statistics, and lattice dynamics as well as applications in polaron theory, electronic gas in a magnetic field, thermodynamics of dielectrics, and magnetic materials in a magnetic field. The text also examines statistical thermodynamics using functional integration and Feynman path integrals. In addition, it features physical results and worked problems.
Statistical Tools for Environmental Quality Measurement (Chapman & Hall/CRC Applied Environmental Statistics)
by Douglas E. Splitstone Michael E. GinevanWhen interpreting environmental data, scientists and engineers first must select the correct statistical tool to use for their analysis. By doing this they will be able to make sound decisions in their efforts to solve environmental problems. They need a detailed reference that points out the subtle differences between statistical procedures, makin
Statistical and Computational Methods in Brain Image Analysis (Chapman & Hall/CRC Mathematical and Computational Imaging Sciences Series)
by Moo K. ChungThe massive amount of nonstandard high-dimensional brain imaging data being generated is often difficult to analyze using current techniques. This challenge in brain image analysis requires new computational approaches and solutions. But none of the research papers or books in the field describe the quantitative techniques with detailed illustratio
Statistical and Condensed Matter Physics
by Serguei N. BurmistrovThe book outlines the fundamentals of statistical and condensed matter physics. The statistical physics is the basis of condensed matter physics and the tool for studying a variety of condensed media in the thermodynamic (heat) conditions. The statistical physics is presented within the framework of canonical Gibbs distribution entailing the relations known from the classical (heat) thermodynamics. The application of the statistical theory embraces such topics as ideal classical and quantum gases, Bose-type excitations, phase transitions and critical phenomena, normal Fermi liquid, superconductivity, weakly non-ideal Bose gases, superfluidity, and magnetism. Each section ends with one or several problems with the solutions clarifying the paragraph content and delivering some additional physical examples. The problems give an opportunity for a reader to check the own real knowledge of the material studied.
Statistical and Inductive Probabilities (Dover Books on Mathematics)
by Hugues LeblancAmong probability theorists, a bitter controversy has raged for decades between the adherents of John Maynard Keynes' A Treatise on Probability (1921) and those of Richard von Mises' "Grundlagen der Wahrscheinlichkeitsrechnung" (1919). Keynes declared that probabilities measure the extent to which a so-called evidence proposition supports another sentence. Von Mises insisted that they measure the relative frequency with which the members of a so-called reference set belong to another set. Statistical and Inductive Probabilities offers an evenhanded treatment of this issue, asserting that both statistical and inductive probabilities may be treated as sentence-theoretic measurements, and that the latter qualify as estimates of the former.Beginning with a survey of the essentials of sentence theory and of set theory, author Hugues Leblanc examines statistical probabilities (which are allotted to sets by von Mises' followers), showing that statistical probabilities may be passed on to sentences, and thereby qualify as truth-values. Leblanc concludes with an exploration of inductive probabilities (which Keynes' followers allot to sentences), demonstrating their reinterpretation as estimates of truth-values.Each chapter is preceded by a summary of its contents. Illustrations accompany most definitions and theorems, and footnotes elucidate technicalities and bibliographical references.
Statistical and Multivariate Analysis in Material Science
by Giorgio LucianoThe present work is an introductory text in statistics, addressed to researchers and students in the field of material science. It aims to give the readers basic knowledge on how statistical reasoning is exploitable in this field, improving their knowledge of statistical tools and helping them to carry out statistical analyses and to interpret the results. It also focuses on establishing a consistent multivariate workflow starting from a correct design of experiment followed by a multivariate analysis process.
Statistical and Nonlinear Physics (Encyclopedia of Complexity and Systems Science Series)
by Bulbul ChakrabortyThis volume of the Encyclopedia of Complexity and Systems Science, Second Edition, focuses on current challenges in the field from materials and mechanics to applications of statistical and nonlinear physics in the life sciences. Challenges today are mostly in the realm of non-equilibrium systems, although certain equilibrium systems also present serious hurdles. Where possible, pairwise articles focus on a single topic, one from a theoretical perspective and the other from an experimental one, providing valuable insights. In other cases, theorists and experimentalists have collaborated on a single article. Coverage includes both quantum and classical systems, and emphasizes 1) mature fields that are not covered in the current specialist literature, (2) topics that fall through the cracks in disciplinary journals/books, or (3) developing areas where the knowledge base is large and robust and upon which future developments will depend. The result is an invaluable resource for condensed matter physicists, material scientists, engineers and life scientists.
Statistical and Thermal Physics: An Introduction
by Michael J.R. HochThermal and statistical physics has established the principles and procedures needed to understand and explain the properties of systems consisting of macroscopically large numbers of particles. By developing microscopic statistical physics and macroscopic classical thermodynamic descriptions in tandem, Statistical and Thermal Physics: An Introduction provides insight into basic concepts and relationships at an advanced undergraduate level. This second edition is updated throughout, providing a highly detailed, profoundly thorough, and comprehensive introduction to the subject and features exercises within the text as well as end-of-chapter problems. Part I of this book consists of nine chapters, the first three of which deal with the basics of equilibrium thermodynamics, including the fundamental relation. The following three chapters introduce microstates and lead to the Boltzmann definition of the entropy using the microcanonical ensemble approach. In developing the subject, the ideal gas and the ideal spin system are introduced as models for discussion. The laws of thermodynamics are compactly stated. The final three chapters in Part I introduce the thermodynamic potentials and the Maxwell relations. Applications of thermodynamics to gases, condensed matter, and phase transitions and critical phenomena are dealt with in detail. Initial chapters in Part II present the elements of probability theory and establish the thermodynamic equivalence of the three statistical ensembles that are used in determining probabilities. The canonical and the grand canonical distributions are obtained and discussed. Chapters 12-15 are concerned with quantum distributions. By making use of the grand canonical distribution, the Fermi–Dirac and Bose–Einstein quantum distribution functions are derived and then used to explain the properties of ideal Fermi and Bose gases. The Planck distribution is introduced and applied to photons in radiation and to phonons on solids. The last five chapters cover a variety of topics: the ideal gas revisited, nonideal systems, the density matrix, reactions, and irreversible thermodynamics. A flowchart is provided to assist instructors on planning a course. Key Features: Fully updated throughout, with new content on exciting topics, including black hole thermodynamics, Heisenberg antiferromagnetic chains, entropy and information theory, renewable and nonrenewable energy sources, and the mean field theory of antiferromagnetic systems Additional problem exercises with solutions provide further learning opportunities Suitable for advanced undergraduate students in physics or applied physics. Michael J.R. Hoch spent many years as a visiting scientist at the National High Magnetic Field Laboratory at Florida State University, USA. Prior to this, he was a professor of physics and the director of the Condensed Matter Physics Research Unit at the University of the Witwatersrand, Johannesburg, where he is currently professor emeritus in the School of Physics.
Statistical and Thermal Physics: Fundamentals and Applications
by M.D. SturgeThis book is based on many years of teaching statistical and thermal physics. It assumes no previous knowledge of thermodynamics, kinetic theory, or probability---the only prerequisites are an elementary knowledge of classical and modern physics, and of multivariable calculus. The first half of the book introduces the subject inductively but rigorously, proceeding from the concrete and specific to the abstract and general. In clear physical language the book explains the key concepts, such as temperature, heat, entropy, free energy, chemical potential, and distributions, both classical and quantum. The second half of the book applies these concepts to a wide variety of phenomena, including perfect gases, heat engines, and transport processes. Each chapter contains fully worked examples and real-world problems drawn from physics, astronomy, biology, chemistry, electronics, and mechanical engineering.
Statistical and Thermal Physics: With Computer Applications
by Harvey Gould Jan TobochnikThis textbook carefully develops the main ideas and techniques of statistical and thermal physics and is intended for upper-level undergraduate courses. The authors each have more than thirty years' experience in teaching, curriculum development, and research in statistical and computational physics. Statistical and Thermal Physicsbegins with a qualitative discussion of the relation between the macroscopic and microscopic worlds and incorporates computer simulations throughout the book to provide concrete examples of important conceptual ideas. Unlike many contemporary texts on thermal physics, this book presents thermodynamic reasoning as an independent way of thinking about macroscopic systems. Probability concepts and techniques are introduced, including topics that are useful for understanding how probability and statistics are used. Magnetism and the Ising model are considered in greater depth than in most undergraduate texts, and ideal quantum gases are treated within a uniform framework. Advanced chapters on fluids and critical phenomena are appropriate for motivated undergraduates and beginning graduate students. Integrates Monte Carlo and molecular dynamics simulations as well as other numerical techniques throughout the text Provides self-contained introductions to thermodynamics and statistical mechanics Discusses probability concepts and methods in detail Contains ideas and methods from contemporary research Includes advanced chapters that provide a natural bridge to graduate study Features more than 400 problems Programs are open source and available in an executable cross-platform format Solutions manual (available only to teachers)
Statistics Done Wrong
by Alex ReinhartScientific progress depends on good research, and good research needs good statistics. But statistical analysis is tricky to get right, even for the best and brightest of us. You'd be surprised how many scientists are doing it wrong.Statistics Done Wrong is a pithy, essential guide to statistical blunders in modern science that will show you how to keep your research blunder-free. You'll examine embarrassing errors and omissions in recent research, learn about the misconceptions and scientific politics that allow these mistakes to happen, and begin your quest to reform the way you and your peers do statistics.You'll find advice on:–Asking the right question, designing the right experiment, choosing the right statistical analysis, and sticking to the plan–How to think about p values, significance, insignificance, confidence intervals, and regression–Choosing the right sample size and avoiding false positives–Reporting your analysis and publishing your data and source code–Procedures to follow, precautions to take, and analytical software that can helpScientists: Read this concise, powerful guide to help you produce statistically sound research. Statisticians: Give this book to everyone you know.The first step toward statistics done right is Statistics Done Wrong.
Statistics Explained
by Steve MckillupAn understanding of statistics and experimental design is essential for life science studies, but many students lack a mathematical background and some even dread taking an introductory statistics course. Using a refreshingly clear and encouraging reader-friendly approach, this book helps students understand how to choose, carry out, interpret and report the results of complex statistical analyses, critically evaluate the design of experiments and proceed to more advanced material. Taking a straightforward conceptual approach, it is specifically designed to foster understanding, demystify difficult concepts and encourage the unsure. Even complex topics are explained clearly, using a pictorial approach with a minimum of formulae and terminology. Examples of tests included throughout are kept simple by using small data sets. In addition, end-of-chapter exercises, new to this edition, allow self-testing. Handy diagnostic tables help students choose the right test for their work and remain a useful refresher tool for postgraduates.
Statistics and Analysis of Scientific Data
by Massimiliano BonamenteStatistics and Analysis of Scientific Data covers the foundations of probability theory and statistics, and a number of numerical and analytical methods that are essential for the present-day analyst of scientific data. Topics covered include probability theory, distribution functions of statistics, fits to two-dimensional datasheets and parameter estimation, Monte Carlo methods and Markov chains. Equal attention is paid to the theory and its practical application, and results from classic experiments in various fields are used to illustrate the importance of statistics in the analysis of scientific data. The main pedagogical method is a theory-then-application approach, where emphasis is placed first on a sound understanding of the underlying theory of a topic, which becomes the basis for an efficient and proactive use of the material for practical applications. The level is appropriate for undergraduates and beginning graduate students, and as a reference for the experienced researcher. Basic calculus is used in some of the derivations, and no previous background in probability and statistics is required. The book includes many numerical tables of data, as well as exercises and examples to aid the students' understanding of the topic.
Statistics and Analysis of Scientific Data
by Massimiliano BonamenteThe revised second edition of this textbook provides the reader with a solid foundation in probability theory and statistics as applied to the physical sciences, engineering and related fields. It covers a broad range of numerical and analytical methods that are essential for the correct analysis of scientific data, including probability theory, distribution functions of statistics, fits to two-dimensional data and parameter estimation, Monte Carlo methods and Markov chains. Features new to this edition include: * a discussion of statistical techniques employed in business science, such as multiple regression analysis of multivariate datasets. * a new chapter on the various measures of the mean including logarithmic averages. * new chapters on systematic errors and intrinsic scatter, and on the fitting of data with bivariate errors. * a new case study and additional worked examples. * mathematical derivations and theoretical background material have been appropriately marked, to improve the readability of the text. * end-of-chapter summary boxes, for easy reference. As in the first edition, the main pedagogical method is a theory-then-application approach, where emphasis is placed first on a sound understanding of the underlying theory of a topic, which becomes the basis for an efficient and practical application of the material. The level is appropriate for undergraduates and beginning graduate students, and as a reference for the experienced researcher. Basic calculus is used in some of the derivations, and no previous background in probability and statistics is required. The book includes many numerical tables of data, as well as exercises and examples to aid the readers' understanding of the topic.
Statistics and Data Analysis for Microarrays Using R and Bioconductor (Chapman & Hall/CRC Computational Biology Series)
by Sorin DraghiciRichly illustrated in color, Statistics and Data Analysis for Microarrays Using R and Bioconductor, Second Edition provides a clear and rigorous description of powerful analysis techniques and algorithms for mining and interpreting biological information. Omitting tedious details, heavy formalisms, and cryptic notations, the text takes a hands-on, example-based approach that teaches students the basics of R and microarray technology as well as how to choose and apply the proper data analysis tool to specific problems.New to the Second EditionCompletely updated and double the size of its predecessor, this timely second edition replaces the commercial software with the open source R and Bioconductor environments. Fourteen new chapters cover such topics as the basic mechanisms of the cell, reliability and reproducibility issues in DNA microarrays, basic statistics and linear models in R, experiment design, multiple comparisons, quality control, data pre-processing and normalization, Gene Ontology analysis, pathway analysis, and machine learning techniques. Methods are illustrated with toy examples and real data and the R code for all routines is available on an accompanying downloadable resource.With all the necessary prerequisites included, this best-selling book guides students from very basic notions to advanced analysis techniques in R and Bioconductor. The first half of the text presents an overview of microarrays and the statistical elements that form the building blocks of any data analysis. The second half introduces the techniques most commonly used in the analysis of microarray data.
Statistics and Scaling in Turbulent Rayleigh-Bénard Convection
by Emily S.C. ChingThis Brief addresses two issues of interest of turbulent Rayleigh-Bénard convection. The rst issue is the characterization and understanding of the statistics of the velocity and temperature uctuations in the system. The second issue is the revelation and understanding of the nature of the scaling behavior of the velocity temperature structure functions. The problem under the Oberbeck-Boussinesq approximation is formulated. The statistical tools, including probability density functions (PDF) and conditional statistics, for studying fluctuations are introduced, and implicit PDF formulae for fluctuations obeying certain statistical symmetries are derived. Applications of these PDF formulae to study the fluctuations in turbulent Rayleigh-Bénard convection are then discussed. The phenomenology of the different types of scaling behavior: the Bolgiano-Obhukov scaling behavior when buoyancy effects are significant and the Kolmogorov-Obukhov-Corrsin scaling behavior when they are not, is introduced. A crossover between the two types of scaling behavior is expected to occur at the Bolgiano length scale above which buoyancy is important. The experimental observations are reviewed. In the central region of the convective cell, the Kolmogorov-Obukhov-Corrsin scaling behavior has been observed. On the other hand, the Bolgiano-Obukhov scaling remains elusive only until recently. By studying the dependence of the conditional temperature structure functions on the locally averaged thermal dissipation rate, evidence for the Bolgiano-Obukhov scaling has recently been found near the bottom plate. The different behaviors observed in the two regions could be attributed to the different size of the Bolgiano scale. What physics determines the relative size of the Bolgiano scale remains to be understood. The Brief is concluded by a discussion of these outstanding issues.
Statistics by Simulation: A Synthetic Data Approach
by Aaron M. Ellison Carsten F. DormannAn accessible guide to understanding statistics using simulations, with examples from a range of scientific disciplinesReal-world challenges such as small sample sizes, skewed distributions of data, biased sampling designs, and more predictors than data points are pushing the limits of classical statistical analysis. This textbook provides a new tool for the statistical toolkit: data simulations. It shows that using simulation and data-generating models is an excellent way to validate statistical reasoning and to augment study design and statistical analysis with planning and visualization. Although data simulations are not new to professional statisticians, Statistics by Simulation makes the approach accessible to a broader audience, with examples from many fields. It introduces the reasoning behind data simulation and then shows how to apply it in planning experiments or observational studies, developing analytical workflows, deploying model diagnostics, and developing new indices and statistical methods.• Covers all steps of statistical practice, from planning projects to post-hoc analysis and model checking• Provides examples from disciplines including sociology, psychology, ecology, economics, physics, and medicine• Includes R code for all examples, with data and code freely available online• Offers bullet-point outlines and summaries of each chapter• Minimizes the use of jargon and requires only basic statistical background and skills